T  K 


HOW  TO   MAKE 
HIGH- PRESSURE 

'RANSFQRMER3 


UC-NI 


SB    317    DEB 


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DO 


E  65  CENTS 


Directions  for 
Designing,  Making,  and 

Operating 
High  -  Pressure  Transformers 


BY 
PROFESSOR  F.  E.  AUSTIN 

/ 

Copyright  1914  by  F.  E.  Austin. 


Professor  and  Head  of  the  Department  of  Electrical  Engineering  in 
the  Thayer  School  of  Engineering,  connected  with  Dartmouth  College, 
Hanover,  N.  H. 

Author  of      "Examples  in  Magnetism." 

"Examples  in  Alternating- Currents." 

"How  to  Make  a  Transformer  for  Low  Pressures." 


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Electrical  Engineering 

GRANT  BLDG.,  ATLANTA,  GA. 


Designing,  Making,  and  Operating  ff-/g^  Pressure. Transformers       3 


TABLE  OF  EQUIVALENTS  OF  LENGTH,  AREA  AND  VOLUME. 

1  INCH  =  2.54  CENTIMETERS. 
1  centimeter  =  7.£  4   =  0  .  393  inch. 

1  SQUARE  INCH  =  2~542  =  6.45  SQUARE  CENTIMETERS. 
1  square  centimeter  =  ^.4-5-  =0.  155  square  inch. 

1  CUBIC  INCH  =  2l>43  =  16.38  CUBIC  CENTIMETERS. 

1  cubic  centimeter  =  TS\^  =  0.06105  cubic  inch. 

1  MIL  =  TflW  of  an  inch. 

1  square  mil  =  area  of  a  square,  1  mil  on  a  side. 

1  circular  mil  =  area  of  a  circle,  1  mil  in  diameter. 

=  area  of  a  circle  °f  an  mcn  in  diameter. 


A  square  mil  is  greater  than  a  circular  mil,  because  the  area  of  a  square 
is  more  than  the  area  of  an  inscribed  circle. 

1  square  inch  =  1000  X  1000  =  1,000,000  square  mils. 
4    V    1  000000 

1  SQUARE  INCH  =    —  ^-^  =  1,274,500  CIRCULAR  MILS. 

7T 

TT  =  3.14159  =  ratio  of  the  circumference  of  any  circle  to  its  di- 
ameter. The  diameter  of  any  circle  multiplied  by  3.14159  =  its  circum- 
ference. 

Square  root  of  2   =  l/2~   =   1.414. 


1  Horse-  power  =  33000  foot-pounds    per    minute  =  ^V0—  =  550    foot- 

pounds per  second  . 
=  746  watts. 

1  Foot-pound  =  1  .  3562  X  107  ergs. 
Volts   X  Amperes   =  Watts. 


346495 


4        Designing,  Making,  and  .Operating   High- Pressure  Transformers 

DIRECTIONS    FOR    DESIGNING,    MAKING,  AND    OPERATING 
A     HIGH-PRESSURE     TRANSFORMER. 

Introductory. 

Electric  power,  at  a  high  pressure,  is  at  present  a  commercial  demand 
and  necessity;  the  considerations  in  favor  of  direct-current  power  at  high 
pressure  are,  with  the  present  forms  of  construction,  fewer  than  those 
favoring  alternating  high  pressure  power.  The  one  consideration  above 
all  others  in  favor  of  "alternating-current"  power,  is  the  simplicity,  and 
economy  with  which  the  alternating-pressure,  (constituting  one  factor 
of  the  power)  may  be  increased  or  decreased  in  magnitude;  or  in  common 
engineering  parlance: — "stepped  up"  or  "stepped  down",  from  a  low  to  a 
high  or  from  a  high  to  a  low  value  respectively. 

The  device  employed  to  accomplish  the  stepping  up  or  stepping 
down  process  is  the  so-called  transformer,  which  is  a  really  wonderful 
piece  of  apparatus,  when  considered  as  an  energy  device. 

It  should  be  remembered  that  a  transformer  cannot  be  operated 
on  direct-current  circuits;  but  only  by  being  connected  with  circuits  in 
which  the  current  is  continuously  undergoing  regular  changes  in  value; 
that  is,  by  alternating-currents. 

The  term  "transformer"  is  perhaps  a  misnomer  when  used  in  con- 
nection with  the  now  common  device;  since  energy  is  not  transformed 
by  the  device  from  one  form  into  another  form;  but  a  certain  percent  of 
the  electrical  energy  supplied  to  the  device  is  given  out  by  it  with  simply 
a  change  in  the  magnitude  of  the  two  factors  of  electrical  power : — pressure 
and  current.  The  device  might  more  aptly  be  called  a  transmuter;  from 
the  Latin  trans  (meaning  across)  and  mutare,  (meaning  to  change  across 
or  to  carry  over) . 

The  electric  power  is  simply  carried  across,  through  the  medium 
of  the  so-called  transformer,  from  one  electric  circuit  to  another. 

A  transformer  might  then  be  defined  as  a  device  for  the  exchange  of 
electric  power  from  one  alternating-current  circuit  to  another,  with  a 
desired  change  in  electric  pressure. 

As  will  be  evident  later,  a  transformer  consists  essentially  of  two  elec- 
tric circuits  interlinked  by  a  magnetic  circuit.  A  chain  consisting  of  three 
links,  the  middle  link  representing  the  magnetic  circuit,  and  the  two  outer 
links  representing  the  two  electrical  circuits;  one  the  primary  and  the 
other  the  secondary.  Since  a  chain  is  no  stronger  than  its  weakest  link,  so 
the  commercial  value  of  a  transformer  is  determined  by  its  weakest  part. 

The  mechanical  simplicity  of  a  transformer  is  remarkable;  containing 
no  moving  parts;  and  although  at  times  receiving  and  delivering  energy 
at  the  rate  of  thousands  of  horse-power,  it  requires  very  little  care  and 
maintenance. 


Designing,  Making,  and  Operating   High-Pressure  Transformers       5 


Fig.  1. 


b. 


There  are  two  general  types  of  transformers  in  use  at  present,  classified 
according  to  their  construction.  One  is  called  the  "shell"  type  the  other 
the  "core"  type. 

The  shell  type  is  shown  at  (a)  figure  1,  page  5,  and  the  core  type  is 
shown  at  (b)  same  figure.  In  the  shell  type  the  iron  core  surrounds  the 
copper  circuit;  while  in  the  core  type  the  copper  circuit  surrounds  the  iron 
core. 


Fig.  2. 


6       Designing,  Making,  and  Operating  High-Pressure  Transjormers 

The  analysis  of  the  physical  phenomena  involved  in  the  operation 
of  a  transformer,  is  as  complex  as  the  device  itself  is  simple. 

A  brief  explanation  of  the  physical  principles  involved  in  the  opera- 
tion of  a  transformer  may  be  useful. 

Suppose  C,  in  figure  2,  denotes  a  number  of  thin  iron  plates,  placed 
one  above  another  to  form  a  rectangular  "core".  These  thin  plates  may 
be  electrically  insulated  from  each  other  by  insulating  paint,  varnish,  or 
simply  by  a  coating  of  iron  rust  that  readily  forms  after  the  plates  have  been 
covered  with  moisture. 

Next  suppose  a  number  of  turns  of  large  size,  cotton  covered,  copper 
magnet  wire,  denoted  by  P,  are  wound  around  one  limb  of  the  core,  and 
a  larger  number  of  turns  of  smaller  cotton  covered  copper  magnet  wire, 
denoted  by  S,  are  wound  around  the  opposite  limb  of  the  core.  There 
is  then  no  electrical  connection  of  any  kind  between  the  two  coils  and  the 
iron  core,  or  between  the  two  coils  themselves 

The  few  turns  of  large  wire,  P,  may  be  designated  as  the  "primary" 
while  the  coil  consisting  of  many  turns  of  small  wire,  denoted  by  S,  may 
be  designated  as  the  "secondary". 

The  primary  in  this  case  has  a  low  resistance,  while  the  secondary 
has  a  much  greater  resistance. 

Suppose  an  alternating-pressure  denoted  by  Ep  is  applied  to  the  ter- 
minals of  the  primary.  An  "alternating-current"  then  exists  in  the  primary 
which  sets  up  an  alternating  magnetic  flux  or  magnetic  field  in  the  iron 
core.  This  alternating  magnetic  flux  induces  a  counter  electromotive 
force  in  the  primary  and  also  induces  an  electromotive  force  in  the  second- 
ary windings.  The  induced  electromotive  force  per  turn  of  wire  is  practic- 
ally the  same  in  both  the  primary  and  the  secondary.  However  the 
(induced)  pressure  Es  between  the  terminals  of  the  secondary  is  n  times 
as  great  as  the  pressure  (Ep),  applied  to  the  terminals  of  the  primary, 
if  the  secondary  turns  are  n  times  as  many  as  the  turns  on  the  primary. 
If  Ep  is  an  alternating  pressure,  then  E8  will  also  be  an  alternating  pressure. 
This  does  not  imply  that  the  shapes  of  the  primary  and  secondary  pres- 
sure curves  are  similar.  Neither  does  it  follow  that  the  shapes  of  the  pri- 
mary and  secondary  currents  are  the  same. 

If  now  the  secondary  terminals  are  connected  with  a  straight  wire 
having  considerable  resistance,  a  current  in  the  secondary  windings  will 
result,  which  is  an  alternating-current  having  the  same  frequency  as  the 
frequency  of  the  applied  primary  pressure.  The  secondary  current  exist- 
ing in  the  secondary  windings,  reacts  to  reduce  very  slightly  the  magnetic 
flux  in  the  core;  this  reduction  of  flux  reduces  the  counter  electromotive 
force  in  the  primary,  allowing  an  increase  in  the  primary  current.  If 


Designing,  Making,  and  Operating  High-Pressure  Transformers        7 

the  resistance  connected  with  the  secondary  is  reduced,  an  increase  of  sec- 
ondary current  results,  with  a  corresponding  increase  of  primary  current. 

The  operation  as  described,  constitutes  inherent  regulation  of  sup- 
ply and  demand,  performed  without  the  movement  of  a  material  substance 
or  of  mass. 

The  primary  acts  as  a  "choke1'  coil,  the  value  of  the  current  in  it  being 
expressed  by : 

E 

IP=   -  p  (1.)     In  this  equation  Ep  denotes  the  applied 

l/R2p+(27r/L)2 

primary  pressure,  in  volts;  Ip  the  primary  current,  in  amperes;  /  denotes 
the  frequency,  in  complete  cycles  per  second,  of  the  applied  pressure,  and 
of  the  primary  current;  Rp  denotes  the  resistance  of  the  primary  winding, 
in  ohms,  and  L  denotes  the  so-called  "coefficient  of  induction,"  expressed 
in  "henrys";  which  is  the  only  variable  in  the  equation. 

To  show  the  effect  the  value  of  L  has  on  the  primary  current,  suppose 
the  following  data  are  given,  to  find  Ip. 

DATA. 

Ep   =  110 'volts  _j      =  3.14159 

/  =  60  cycles.  R2P   =  T^ 

RP   =  iV  onm-  27r/L    =  377  (very  nearly) . 

L     =   1  henry. 


110  110 

Thenln   = 


1/TtJo    +  3772        1/142129.01 

=   0.29  ampere. 

If  to  this  primary  winding  a  direct-current  pressure  of  110  volts  should  be 

applied,  the  result  ing  current  would  be:     Ip   =  -        =    1100   AMPERES, 

i* 

which  would  have  been  the  same  with  the  alternating-pressure  of  110  volts, 
if  the  primary  wire  had  been  laid  out  straight  with  no  iron  near  it. 

This  shows  the  "choking"  effect,  on  alternating-currents,  of  coiling  a 
wire  around  an  iron  core,  and  the  primary  of  a  transformer  is  said  to  act 
as  a  "choke"  coil. 

To  explain  somewhat  differently  a  few  of  the  important  functional 
phenomena  occurring  during  the  operation  of  a  transformer,  a  brief  outline 


8       Designing,  Making,  and  Operating  High-Pressure  Transformers 

treating  of  a  particular  case  in  designing,  is  included  in  the  following  dis- 
cussion applying  to  transformers. 

While  it  is  possible  the  mathematical  discussion  may  not  be  com- 
pletely comprehended  by  one  who  has  had  only  a  limited  training  in 
"mathematics",  it  is  hoped  that  everyone  may  obtain  valuable  informa- 
tion regarding  the  general  principles  of  transformer  operation  by  carefully 
studying  this  portion  of  the  text. 

For  the  benefit  of  those  desiring  to  build  a  high  pressure  transformer 
for  experimental  use,  such  as  for  wireless  telegraphy,  for  the  production 
of  "ozone"  or  for  vacuum  tube  lighting,  data  applying  to  specific  cases 
are  given. 

If  however,  one  studies  carefully  the  general  principles,  many  varia- 
tions from  the  given  conditions  may  be  readily  effected,  to  meet  a  large 
range  of  requirements. 

The  matter  headed  "CAUTION"  and  "PRECAUTION"  should 
be  very  carefully  read  by  everyone  who  builds  or  who  operates  a  high- 
pressure  transformer. 

SYMBOLS  AND  NOTATION.      . 

Since  electric  power  is  often  expressed  in  terms  of  the  two  factors, 
pressure  and  current,  denoted  by  E  X  I,  (meaning  the  product  of  a  pres- 
sure, in  volts,  by  a  current,  in  amperes)  if  that  portion  (or  link)  of  the  trans- 
former to  which  the  electric  energy  is  supplied  is  designated  as  the  "pri- 
mary1', while  that  portion  (or  link)  from  which  electric  energy  is  delivered 
is  called  the  "secondary",  the  following  symbols  and  notation  will  be  adopt- 
ed. 

Ep  denotes  the  pressure,  in  volts,  applied  to  the  primary  circuit. 

Es  denotes  the  pressure,  in  volts,  available  from  the  secondary  circuit. 

IP  denotes  the  current,  in  amperes,  in  the  primary  circuit. 

I8  denotes  the  current,  in  amperes,  in  the  secondary  circuit. 

Rp  denotes  the  resistance,  in  ohms,  of  the  primary  circuit. 

R8  denotes  the  resistance,  in  ohms,  of  the  secondary  circuit. 

Wp  denotes  the  power  input,  in  watts,  to  primary  circuit. 

Wu  denotes  the  useful  power  output,  in  watts,  from  secondary. 

?7  (Greek  letter  eta)  denotes  the  so-called  commercial  efficiency  of  a 
transformer. 

W 

Then :    77    =  — —  ;  (2) :  being  a  symbolic  expression  for  the  commercial 
Wp 

power  efficiency  of  any  transformer. 

The  commercial  power  efficiency  of  a  transformer  is  the  ratio  of 
the  useful  power  output  to  the  total  power  input. 


Designing,  Making,  and  Operating  High-Pressure  Transformers       9 

If  a  transformer  is  operating  a  load  consisting  of  incandescent  lamps, 
as  is  common  practice,  then  the  commercial  efficiency  of  the  transformer 
might  be  expressed  by: 

^•(3) 

Wp'(< 

If  the  output  from  a  transformer  is  increased,  the  input  must  also  be 
increased.  The  input  has  always  to  supply  the  output  plus  all 

LOSSES  IN  A  TRANSFORMER. 

The  losses  in  a  transformer  may  be  divided  into  the  "copper 
and  the  "core  losses".  The  copper  losses  may  be  still  further  divided  into 
the  loss  in  the  primary  windings  and  the  loss  in  the  secondary  windings. 
These  are  the  so-called  RI2  losses,  in  watts.  The  primary  loss  would  be 
expressed  by  RPIP2  and  the  secondary  loss  by  RSIS2.  The  resistances  Rp 
and  Rs  of  the  primary  and  secondary  coils  respectively,  are  constants*; 
while  the  currents  denoted  by  Ip  and  Is  are  variables-  The  copper  losses 
are  therefore  variables,  depending  upon  the  load  output.  If  there  is  no 
load  output,  then  Is  is  zero  and  Rsla2  is  also  zero.  If  the  transformer  has 
its  primary  connected  with  service  mains,  even  with  no  load  output,  there 
will  be  some  RPIP2  loss  in  the  primary.  However  under  this  condition, 
the  primary  current  Ip  is  very  small;  less  than  unity,  so  that  the  square  of 
the  current  will  be  still  less,  f  numerically,  and  Rp  being  not  much  greater 
than  unity,  (usually  less  than  unity)  the  RPIP2  loss  for  small  transformers, 
is  usually  less  than  one  watt  at  no  load  secondary.  When  however  a  load 
is  applied  to  the  secondary,  then  the  RSIS2  loss  in  the  secondary  becomes 
appreciable,  the  RPID2  loss  in  the  primary  increases,  and  the  total  copper 
loss  becomes  large  enough  to  be  a  considerable  proportion  of  the  total 
power  input.  It  is  evident  then  as  the  load  output  increases,  the  primary 
and  secondary  currents  increase,  causing  the  total  copper  loss,  expressed 
by  Rplp2  +  RSIS2  to  increase. 

CORE  LOSSES  IN  A  TRANSFORMER. 

The  so-called  "core  loss"  in  a  transformer  may  be  diyided  into  the 
"eddy  current"  loss  and  the  "hysteresis"  loss.  The  eddy  current  loss  is  an 
R  I2  loss,  produced  by  currents  induced  in  the  iron  core  by  the  primary 
input.  To  reduce  the  eddy  currents,  and  the  eddy  current  loss,  the  core  is 


*So  long  as  the  temperature  of  the  coils  remains  constant. 

fFor  example,  3  is  less  than  unity,  and  the  square  of  \  is  J;  less  than  \.     Likewise  the 
square  of  |  is  T55;  which  is  less  than  f . 


10      Designing,  Making,  and  Operating  High-Pressure  Transformers 

made  "laminated",  built  up  of  thin  plates  of  iron,  insulated  from  each  other; 
usually  by  varnish. 

The  hysteresis  loss  is  a  heat  loss  produced  by  the  reversals  of  the 
molecules  of  the  iron  in  the  core  when  the  magnetism  of  the  core  is  reversed; 
which  happens  every  time  the  current  in  the  primary  is  reversed;  for  a  60 
cycle  circuit,  this  happens  120  times  every  second.  That  is,  the  molecules 
are  turned  end  for  end  120  times  every  second.  Such  rapid  movement  of 
molecules  produces  heat,  as  though  the  iron  were  hammered  rapidly  with  a 
hammer;  as  may  be  done  by  placing  an  iron  nail  on  a  rock  or  on  an  anvil 
and  hammering  it  rapidly.  The  only  method  adopted  to  reduce  the  hy- 
steresis loss,  is  to  use  a  "soft"  iron,  or  one  having  a  small  hysteretic  coeffi- 
cient. 

LOSS    DUE    TO    HYSTERESIS. 


The  numerical  values  of  hysteretic  loss,  per  cubic  inch  of  iron  in  the 
core,  as  well  as  for  any  frequency  /,  or  flux  density  33,  may  be  calculated 
from  the  equation  : 

"I  A 


^=7-  K/+231'6;  (4)  in  whic!Tw"Q  denotes  the  loss  in  watts;  /the 

frequency  of  the  supply  pressure,  in  cycles  per  second;  33  the  flux  density  in 
gausses,  or  maxwells  per  square  centimeter,  and  K  denotes  what  is  called 
a  hysteretic  coefficient,  which  varies  for  different  kinds  or  qualities  of  iron. 
For  ordinary  transformer  steel,  K  =  .  0021. 


Maximum  In- 
duction per 
Square  Inch 

Maximum 
Induction 
per  Square 
Centime- 
ter 
in  Gausses 

Loss  in 
Ergs  per 
Cycle  per 
Cubic 
Inch  of 
Iron 

Loss  in 
Watts,  at 
/=15  Cycles 
per  Second, 
per  Cubic 
Inch  of  Iron 

Loss  in 
Watts,  at 
/=25  Cycles 
per  Second, 
per  Cubic 
Inch  of 
Iron 

Loss  in 
Watts,  at 
/=60  Cycles 
aer  Second, 
per  Cubic 
Inch  of 
Iron 

Loss  in 
Watts,  at 
/=100 
Cycles 
per 
Second, 
per  Cubic 
Inch    of 
Iron 

6451.6 

1000 

2170. 

.003255 

.00542 

.01402 

.0217 

12903.2 

2000 

6879. 

.01031 

.01719 

.04127 

.0688 

19354.8 

3000 

13104. 

.01965 

.03276 

.07862 

.1310 

25806.4 

4000 

20147  . 

.03022 

.05038 

.1208 

.2015 

32258.0 

5000 

27846. 

.04176 

.06961 

.1670 

.2784 

38709.6 

6000 

36036. 

.05716 

.09528 

.2286 

.3811 

45161.2 

7000 

45208  . 

.07311 

.1218 

.2924 

.4864 

51612.8 

8000 

56511. 

.09070 

.1511 

.3628 

.6047 

58064.4 

9000 

68796. 

.1094 

.1724 

.4379 

.6899 

64516 

10000 

81900 

.1296 

.2160 

.5184 

.864 

Designing,  Making,  and  Operating   High-Pressure  Transformers      11 


From  inspection  of  the  equation  and  the  values  in  the  table  it  may  be 
seen  that  the  loss  due  to  hysteresis  increases  in  proportion  to  the  increase 
in  frequency,  but  not  in  proportion  to  the  increase  in  flux  density.  33  is 
raised  "to  the  1.6  power,  which  may  be  done  by  the  use  of  logarithms,  as 
shown  on  page  25. 

All  of  the  losses  in  a  transformer  are  in  reality  heat  losses;  a  certain 
portion  of  the  energy  supplied  to  the  transformer  in  the  form  of  electrical 
energy,  is  effective  in  doing  useful  or  desired  work,  while  a  certain  portion 
is  unavoidably  changed  into  non-useful  heat. 

In  designing  transformers,  the  aim  is  to  keep  the  losses  as  small  as 
possible  consistent  with  the  cost  of  construction. 

The  efficiency  rj  does  not  vary  in  direct  proportion  with  the  output, 
since  the  copper  losses  in  a  transformer  are  not  constant  for  all  loads. 

If  the  input  and  the  output  of  any  given  transformer  be  measured 
simultaneously  by  the  proper  instruments,  connected  as  indicated  in  figure 
3,  page  12,  and  the  output,  in  watts,  be  plotted  horizontally,  while  the  corres- 
ponding values  of  the  commercial  efficiency,  calculated  from  equation  (3) , 
page  9,  are  plotted  vertically  as  indicated  in  figure  4,  page  13;  the  result, 
shows  the  variation  in  the  efficiency  for  different  outputs.  The  curve  in 
figure  4  shows  the  result  of  a  test  of  a  TV  kilowatt  (about  \  horse-power) 
transformer  designed  to  transform  from  110  volts,  60  cycles,  to  about  60 
volts,  60  cycles.  This  transformer  is  shown  at  d  and  at  e  in  figure  5. 


Fig.  5. 

The  condition  expressed  by:  Wu  =  ESIS,  exists  only  for  a  nonin- 
ductive  load,  such  as  lamps  or  a  liquid  resistance,  or  any  wire  resistance  not 
wound  in  the  form  of  coils. 

The  condition  is  changed  if  the  load  consists  of  motors,  these  being 
highly  inductive. 


12      Designing,  Making,  and  Operating   High- Pressure  Transformers 


Designing,  Making,  and  Operating  High-Pressure  Transformers      13 


Output  in  Per  Gent,  and  Pressure  in  Volts. 


14  Designing,  Making,  and  Operating  High-Pressure  Transformers 

When  there  is  no  useful  output  from  a  transformer,  there  may  be  some 
input,  to  supply  the  core  losses,  which  are  however  not  large,  and  moreover 
are  to  be  considered  constant  irrespective  of  loads.  That  is,  the  power  loss 
due  to  the  core,  is  the  same  at  no  useful  load  output  as  at  full-load  or  at  any 
over-load  output. 

This  core-loss  means  a  constant  source  of  expense,  if  a  transformer  is 
kept  connected  to  service  mains  when  not  supplying  power  output.  While 
the  core-loss,  expressed  in  watts,  may  not  be  large,  the  watt-hour  expense 
may  be  considerable  if  the  transformer  is  connected  with  the  service  mains 
during  a  long  time.  The  expense  incurred  in  using  electrical  power  de- 
pends upon  two  conditions,  the  RATE  at  which  electricity  is  used,  and  the 
interval  of  time  during  which  it  is  used. 

To  illustrate  this  feature,  suppose  the  core-loss  of  a  transformer  is 
found  by  measurement  to  be  65  watts.  If  the  transformer  is  connected 
with  the  service  mains  for  10  hours  while  furnishing  no  useful  output,  the 
total  energy  used  will  be  65  X  10  =  650  watt  hours,  which  at  a  price  of 

15  cents  per  KILOWATT  HOUR  (per  1000  watt-hours)  will  cost  yV^   X 
15   =  9f  cents.     If  the  transformer  is  connected  all  day,  (24  hours)  the 

65   X  24 

cost  of  the  core-loss  will  be X  15   =  23 . 4  cents. 

1000 

This  is  an  important  consideration  for  the  experimenter  who  uses 
transformers,  when  the  energy  he  uses  is  registered  by  meter,  and  shows 
the  value  of  a  switch,  to  throw  the  primary  out  of  circuit  except  when  act- 
ually needed  to  produce  a  useful  output. 

In  almost  all  experimental  work  with  high  pressure  (step-up)  trans- 
formers, it  will  be  advisable  to  connect  a  double-pole  "knife"  switch  with 
the  primary,  so  that  when  this  switch  is  opened,  the  useful  load  is  dis- 
connected without  danger  of  shocks  to  the  operator  and  at  the  same  time 
the  no-load  core-loss  is  eliminated. 

POWER  FACTOR. 

Consulting  figure  3,  page  2,  again,  to  note  the  arrangement  of  the 
voltmeter,  the  ammeter,  and  the  wattmeter  in  the  primary  circuit,  a  few 
words  explaining  the  meaning  of  "power  factor"  may  not  be  amiss. 

If  the  primary  pressure,  Ep,  applied  to  the  primary  coils  of  a  transform- 
er were  a  direct-pressure  (direct-current  pressure)  the  product  of  the  volt- 
meter indication  and  the  ammeter  indication  would  be  the  same  as  the 
indication  of  the  wattmeter;  if  all  the  instruments  gave  correct  indications. 
The  current  in  the  primary  coils  would  then  be  expressed  by: 


Designing,  Making,  and  Operating   High-Pressure  Transformers      15 


•pi 

IP   =  -^-  according  to  Ohm's  law,  and  the  indication  of  the  wattmeter 
RP 

by:  Wp  =  Eplp.  The  direct-current  in  the  primary  coil  would  however 
have  no  effect  on  the  secondary  coil. 

When  however  the  pressure  applied  to  the  primary  is  an  alternating- 
pressure,  the  indication*  of  the  wattmeter  is  no  longer  the  same  as  the 
product  of  the  voltmeter  and  ammeter  indications,  but  is  found  to  be  less. 

In  such  a  case  the  true  input  in  watts  is  indicated  by  the  wattmeter, 
and  the  relation  would  be  expressed  by: 

Wp  =  Eplp  X  power  factor]  or  as  is  sometimes  expressed:  Wp  = 
Eplp  X  P.  F.  (5)  (P.  F.  stands  for  power  factor).  From  either  of 
these  expressions  is  obtained: 

W 

Power  Factor-  =     —  —  ,    (6)     Since  the   product    EPIP  is  usuallv 
Eplp 

greater  than  Wp,  the  power  factor  is  usually  less  than  unity.  The  product 
Eplp  can  never  be  greater  than  Wp,  and  the  power  factor  can  never  be 
greater  than  unity. 

The  power  factor  may  vary  as  the  load  varies. 

Returning  to  the  consideration  of  efficiency  as  expressed  by  equation 

E  I 

(2)  page  9,  this  may  be  expressed  by  :  rj   =   —  —  —  —  —  —   ;  (7)  . 

Eplp  X  P.  F. 

Now  suppose  that  the  secondary  pressure  is  exactly  equal  to  the  primary 

pressure,  then  the  efficiency  may  be  expressed  by  rj   =    •-  —    8          ;  (7a)  . 

Ip   X  P.  Jr. 

It  is  a  well  known  and  commonly  accepted  fact  that  the  EFFI- 
CIENCY of  any  electrical  device  IS  ALWAYS  LESS  THAN  UNITY; 
that  is  the  per  cent  efficiency  is  always  less  than  100%. 

Since  the  P.  F.  is  never  greater  than  unity  and  since  77  must  always  be 
less  than  unity  it  is  evident  from  the  last  equation  that  in  a  transformer, 
when  the  primary  and  secondary  pressures  are  equal,  the  secondary  cur- 
rent will  always  be  less  than  the  primary  current. 

Furthermore  it  may  be  noted  that  although  the  primary  pressure  and 
secondary  pressure  bear  a  certain  definite  relation  to  one  another  the  same 


*When  dealing  with  instrument  indications  as  in  this  discussion  the  indications  must 
be  noted  simultaneously;  all  taken  at  the  same  instant. 


16      Designing,  Making,  and  Operating  High-Pressure  Transformers 

proportionate  relation  cannot  exist  between  the  secondary  and  primary 
currents,  even  if  the  power  factor  is  unity. 

If  the  efficiency  is  high;  nearly  unity  or  nearly  100%,  the  propor- 
tionality of  currents  and  pressures  is  more  nearly  the  same.  For  many 
practical  considerations  the  proportionality  is  assumed  to  be  the  same. 
This  will  be  made  clearer  by  consideration  of  the  following : 

RATIO  OF  TRANSFORMATION:  The  so-called  ratio  of  trans- 
formation has  reference  to  the  ratio  of  the  secondary  to  the  primary  pres- 
sure. The  primary  is  that  portion  of  a  transformer  to  which  the  primary 
pressure  is  applied,  and  the  secondary  is  that  portion  of  the  transformer 
producing  the  secondary  pressure.  It  should  be  noted  that  the  primary 
pressure  may  be  greater  (as  in  a  step-down  transformer)  than  the  secondary 
pressure.  The  best  definition  of  the  primary  of  a  transformer  is,  that 
portion  of  a  transformer  receiving  energy;  this  having  no  reference  to  pres- 
sures. 

In  any  case  the  ratio  of  transformation  may  be  expressed  as: 

RATIO  OF  TRANSFORMATION   = 

SECONDARY  PRESSURE,  IN  VOLTS  Es 


PRIMARY     PRESSURE,     IN  VOLTS  Ep 

As  an  example,  suppose  it  is  desired  to  find  the  ratio  of  transformation 
of  a  transformer,  if  the  applied,  primary  pressure  is  2200  volts  and  the 
secondary  pressure  is  110  volts. 

RATIO  OF  TRANSFORMATION  =  T&&  =  ^  =  0.5;  or  the 
transformation -is  a  20  to  1  (step-down)  transformation. 

Again,  suppose  the  primary  pressure  is  110  volts  and  the  secondary 
pressure  is  20,000  volts,  then  the  RATIO  OF  TRANSFORMATION  = 
_2.ooo_o  =  iooo.  =  181.81;  or  the  transformation  is  an  11  to  2000  trans- 
formation. 

When  the  ratio  of  transformation  is  greater  than  unity,  the  trans- 
former is  called  a  "step-up"  transformer;  when  less  than  unity,  it  is  called 
a  "step-down"  transformer. 

If  there  were  no  losses  in  a  transformer,  then  the  currents  in  the  pri- 
mary and  secondary  coils  would  be  in  exact  inverse  ratio  to  each  other  as 
compared  with  their  corresponding  primary  and  secondary  pressures, 
But  as  indicated  by  equations  (7)  and  (7a),  page  15,  such  exact  relation 
cannot  exist. 

Let  it  be  supposed  that  Eg  =  n  times  Ep,  then  equation  (7),  page  15 
may  be  written: 


Designing,  Making,  and  Operating  High-Pressure  Transformers      17 


Efficiency,     r,  =  _    (9);  (E3  =  nEp.) 

Jc/plp    X    *  .  r  • 

or  IL.  _     "  x  p-  F-    or  Is  _    J?  ,  x  p.  F.  (10). 

IP  n  n 

That  is,  when  the  secondary  pressure  is  n  times  the  primary  pressure, 
the  secondary  current  is  not  exactly  (^)  one  nth.  of  the  primary  current; 
since  17  X  P.  F.  is  always  less  than  unity. 

For  ordinary  purposes,  however,  the  proportional  relations;  if  Es  = 
nEp  then  I8  =  (J)IP;  may  be  used  without  great  error.  It  should  be 
remembered  however  that  if  Es  is  exactly  n  times  Ep,  ls  is  always  slightly 
more  than  jf  of  Ip,  in  actual  practice. 

It  is  evident  at  this  point  in  the  discussion,  just  why  the  transformer 
is  so  valuable  as  an  intermediate  device  in  the  process  of  power  transmis- 
sion. By  stepping  the  pressure  up,  the  current  may  be  stepped  down,  so 
that  for  transmitting  a  given  power,  much  less  line  copper  is  necessary, 
when  the  power  is  delivered  at  a  high  pressure,  (small  current)  than  when 
the  same  power  is  delivered  at  a  low  pressure.  With  the  smaller  current 
the  HI2  line  loss  is  greatly  reduced.  Interest  on  investment  of  copper  is 
rendered  much  less  by  using  the  transformer. 

DESIGNING  A  20,000  VOLT  TRANSFORMER. 

In  designing  a  transformer  as  in  designing  many  electrical  devices, 
different  requirements  as  to  the  operative  conditions  will  necessitate  dif- 
ferent methods  in  designing. 

A  brief  outline  applying  to  the  design  of  a  transformer  will  be  pre- 
sented herewith  that  may  serve  as  a  guide  in  varying  the  manufacture  of 
the  transformer,  for  which  working  directions  are  given,  beginning  on 
page  26.  The  method  here  adopted  is  not  a  rigorous  mathematical  treat- 
ment, but  one  designed  to  emphasize  practical  applications.  As  a  matter 
of  fact  designs  are  usually  figured  out  on  the  assumption  that  the  alter- 
nating-pressures and  currents  are  sine-waves,  while  they  are  seldom  such 
shapes  in  practice.  Deviation  from  a  sine-wave  form  affects  the  whole 
matter  of  transformer  design  and  operation.  The  considerations  in  this 
book  will  be  on  the  assumption  of  sine-wave  forms. 

The  following  outline  will  apply  to  a  1  K.  W.  or  1000  watt  output, 
"step-up"  transformer,  transforming  110  volts,  at  60  cycles,  to  20,000  volts, 
necessarily  at  the  same  frequency. 

The  ratio  of  transformation  is  2-TT^p_   =   181 .8.     See  page  16. 


r 
18     Designing,  Making,  and  Operating  High-Pressure  Transformers 

The  primary  current  will  be  assumed  as  10  amperes,  and  the  second- 
ary current  as  .05  ampere. 

The  core  losses  and  the  full-load  copper  losses  in  the  transformer  will 
be  assumed  to  be  equal  to  a  total  of  75  watts,  and  the  copper  losses  to  be 
equal  to  50  watts.  This  means  that  the  efficiency  of  the  transformer  is 
to  be  93%.  The  output  being  1000  watts  and  the  input  being  ^°f§  = 
1075 . 1  watts.  The  core  losses  will  evidently  be  25  watts  total.  The  core 
losses  consist  of  the  so-called  eddy-current  loss  and  the  hysteresis  loss; 
while  the  copper  losses  are  the  RI2  losses  in  both  the  primary  and  the 
secondary  coils. 

The  resistances  of  the  primary  and  secondary  may  be  readily  cal- 
culated, for  any  assumed  current,  if  the  loss  in  the  primary  and  in  the 
secondary  coils  is  given. 

The  primary  loss  in  watts  is  denoted  by  RPIP2. 

The  secondary  loss  in  watts  is  denoted  by_RsT82. 

Under  the  given  conditions  RPIP2  +  Rgls2   =  50  watts. 

RESISTANCE  OF  PRIMARY  WINDINGS. 

Although  the  sum  of  the  primary  and  the  secondary  losses  is  to  be  50 
watts,  the  two  losses  are  not  necessarily  equal  to  each  other.  It  will  be 
advisable  to  allow  a  less  loss  for  the  primary  than  for  the  secondary. 

For  the  case  under  consideration  the  loss  for  the  primary  will  be  as- 
sumed as  20  watts;  while  that  for  the  secondary  will  be  assumed  as  30 
watts. 

Since  the  loss  in  the  primary  windings  is  to  be  20  watts,  then: 

20 

Rplp2   =  20,  and  Rp   =  -=?  =   T2^   =  0.2  ohm,  the  required  re- 
102 

sistance  of  the  primary  windings. 

NUMBER  OF  TURNS  IN  THE  PRIMARY  WINDINGS. 

At  this  point  it  will  be  necessary  to  present  what  is  called  the  funda- 
mental equation  of  the  transformer.  Expressed  in  symbols  this  is: 

Ep  =  -°  P  -  — ;  (11)  in  which  Ep  denotes  the  alternating- 
pressure,  expressed  in  volts,  applied  to  the  primary;  Ac  denotes  the  area, 
expressed  in  square  centimeters,  of  the  cross  section  of  the  iron  core;  Np 
denotes  the  number  of  turns  in  the  primary  windings;  /  denotes  the  fre- 
quency, in  cycles  per  second,  of  the  applied  pressure,  and  33  denotes  the 
number  of  magnetic  lines  of  force  set  up  in  the  core  per  square  centimeter 
of  cross  section  of  the  iron  core. 


Designing,  Making,  and  Operating  High-Pressure  Transformers      19 

So  far  as  the  assumptions  already  made  are  concerned,  there  are  three 
unknowns  in  this  equation;  Ac,  ND,  and  33.  Ep  =  110  volts,  /  =  60, 
and  27r  =  2  X  3.1416. 

If  values  are  assumed  for  Ac  and  33  the  equation  may  be  solved  for  the 
value  of  Np;  the  number  of  turns  of  wire  in  the  primary  windings. 

It  is  not  advisable  to  allow  the  value  of  $8  to  exceed  5000  gausses 
(magnetic  lines  per  square  centimeter)  in  transformer  operation. 

It  is  plain  that  the  greater  the  value  assumed  for  33,  the  less  number  of 
turns  will  be  required,  and  the  less  iron  required  for  the  core. 

Let  33   =  3000  and  Ac   =  44.4  centimeters.     Then: 

108  X  Ep 11,000,000,000 

P   "        l/27r/33Ac~     =   1-414   X  3.1416   X    60    X    3000  X  44.4 
=  300  TURNS. 

DATA. 

108  =   100,000,000. 
Ep   =   110  volts. 

/  =     60  cycles  per  second. 
]/2   =   1.414;    1/27T    =  4.44;    1/2  */  =  266.53. 

LENGTH  OF  THE  PRIMARY  WINDINGS. 

If  the  cross  section  of  the  iron  core  is  to  be  44.4  square  centimeters 
it  will  be  f  Jff  =6.89  square  inches. 

If  the  core  is  to  be  square  in  cross  section,  the  length  of  one  side  must 
be  J/6. 89  =  2. 6  inches.  The  distance  around  the  core  will  be  4  X  2 . 6 
=  10.4  inches. 

The  length  of  a  mean  turn  of  the  primary  must  be  more  than  this,  say 
11  inches.  If  there  are  300  turns  in  the  primary  windings  the  total  length 
will  be  300  X  11  =  3300  incites  or  -3-f  ^  =  275  feet. 

SIZE  OF  THE  PRIMARY  WIRE. 

If  the  resistance  of  the  primary  is  to  be  T2^  ohm,  (page  18)  and  its 
length  275  feet,  the  resistance  per  foot  must  be  %j f  =  0 . 000727  ohm. 

Consulting  the  table  on  page  21  column  headed  I,  the  nearest  size 
of  Brown  &  Sharp  gauge  wire  is  found  to  be  a  No.  9  wire. 

WEIGHT  OF  THE  PRIMARY  WINDINGS. 

Since  No.  9  B.&  S.  gauge  double  cotton  covered  round  copper  wire 
weighs  0 . 0404  pound  per  foot  in  length,  the  weight  of  the  complete  primary 
winding  will  be  0 . 0404  X  275  =  11.1  pounds. 


20      Designing,  Making,  and  Operating  High-Pressure  Transformers 

DATA  APPLYING  TO  THE  SECONDARY. 
NUMBER  OF  TURNS  IN  SECONDARY  WINDINGS. 

The  ratio  of  transformation  being  181.8  and  the  number  of  primary 
turns  being  300,  the  minimum  number  of  turns  required  for  the  secondary 
would  be  181.8  X  300;  but  if  the  ratio  of  currents  is  assumed  inversely 
as  the  pressure  ratios,  then  there  must  be  more  than  the  proportionate 

181    8     V     °iOO 

ratio  of  turns.     At  least : =  58645  TURNS.     58650  MAY 

.  9o 

BE  ALLOWED. 

RESISTANCE  OF  SECONDARY  WINDINGS. 

Since  the  loss  in  the  secondary  has  been  assumed  at  30  watts,  then  the 
resistance,  in  ohms,  of  the  complete  secondary  windings  will  be: 

on  OA 

R3  =  ^2   =  -    =   12,000  ohms. 

.052         .0025 

LENGTH  OF  THE  SECONDARY  WINDINGS. 

The  current  density  assumed  for  the  secondary  wire  being  1032  am- 
peres per  square  inch,  which  has  been  found  to  be  a  safe  value,  from  the 
relation, 

—•   =   1032,  the  area   of   the   secondary   wire  will  be  As    =    j^W   or 

Aa 

.00004845  square  inch. 

The  area  of  this  wire,  in  circular  mils,  will  be,  .00004845  X  1,274,500 
=  61.7  CIRCULAR  MILS.  (Seepages.) 

The  nearest  B.  &  S.  gauge  wire  is  a  No.  32,  (see  table  page  21,  column 
D.)  which  will  be  used. 

If  No.  32  B.  &  S.  gauge  is  used  and  the  total  resistance  of  the  secondary 
is  to  be  12000  ohms,  the  possible  number  of  feet  will  be: 

12000  =  74165  FEET.  (From  column  I  page  21,  No.  32  wire  has 
a  resistance  of  .  1618  ohm  per  foot.) 

WEIGHT  OF  SECONDARY  WINDINGS. 

Consulting  table  on  page  21,  column  headed  G,  the  weight  of  double 
cotton  covered,  32  B.  &  S.  is  seen  to  be  .222  pound  per  1000  feet.  The 
total  weight  required  in  the  present  case  is  .222  X  74.16  =  16^ 
POUNDS. 


Designing,  Making,  and  Operating   High-Pressure  Transformers 


22     Designing,  Making,  and  Operating  High-Pressure  Transformers 
DESIGNING  THE  IRON  CIRCUIT. 

The  iron  circuit  of  a  modern  transformer  consists  of  thin  plates  of  soft 
steel,  sometimes  called  "transformer  steel",  laid  one  upon  another  to  form 
an  iron  core  of  the  desired  thickness;  denoted  by  C  in  figure  2,  page  5  and 
figure  17,  page  37.  The  plates  are  usually  coated  all  over  with  some  kind 
of  insulating  varnish,  to  insulate  each  plate  from  the  ones  next  to  it;  thus 
reducing  the  loss  due  to  so-called  "eddy-currents";  (also  called  "foucault 
currents"). 

While  joints  are  undesirable,  so  far  as  losses  in  the  iron  magnetic 
circuit  are  concerned,  it  is  very  difficult  to  construct  a  high-pressure  trans- 
former without  joints,  and  a  magnetic  circuit  without  joints  increases  the 
first  cost  of  material,  because  of  the  waste  material  in  stamping  the  plates, 
and  increases  the  cost  of  labor  in  assembling. 

The  softer  the  iron  or  steel  that  is  used  for  the  core,  the  less  the  loss 
due  to  "hysteresis".  Ordinary  iron  plates  may  have  their  magnetic 
qualities  improved  by  "annealing";  heating  them  to  a  red  heat  and  allow- 
ing them  to  cool  very  slowly  while  protected  from  the  air  by  being  covered 
with  ashes.  Hysteresis  loss  being  due  to  the  reversal  of  the  molecules  of 
the  iron  when  the  current  in  the  primary  coils  is  reversed,  if  the  frequency 
of  the  primary  current  is  increased,  the  molecules  of  iron  have  their  position 
reversed  more  times  each  second,  and  the  more  rapid  motion  of  the  mole- 
cules has  the  effect  of  increasing  the  heating  of  the  iron  core;  as  more  rapid 
hammering  would  have.  The  higher  the  frequency  the  greater  the  "hy- 
steric" loss. 

The  heating  of  the  core  means  the  appropriation  of  a  portion  of  the 
energy  input  to  the  transformer  that  is  therefore  not  available  for  useful 
output,  and  which  should  be  kept  down  to  as  small  an  amount  as  possible. 


Designing,  Making,  and  Operating  High-Pressure  Transformers     23 
NUMBER  OF  IRON  PLATES  FOR  GORE. 

If  the  core  is  built  up  of  plates  2£  inches  wide;  one  set  being  12*  inches 
long  and  the  other  set  1\  inches  long  as  indicated  in  figure  6,  the  plates 
being  TtJ$u  of  an  mcn  (15  mils)  thick,  it  would  require  about  168  sheets 
placed  together  flatwise  to  build  up  to  a  thickness  of  2*  inches.  With  a 
width  of  2*  inches  the  thickness  should  be  slightly  over  2*  inches  (2f 
inches)  to  make  the  cross  section  of  the  core  6.89  square  inches  as  stated 
on  page  19. 

As  will  be  shown  later,  on  page  25,  this  cross  section  is  slightly  less 
than  is  necessary  to  give  the  volume  of  iron  for  continuous  operation  at 
full-load  under  the  assumed  conditions. 

There  will  be  needed,  2  X  183  =  376  sheets  12*"  by  2*"  by  15 
mils  thick,  and  the  same  number  of  sheets  7*"  by  2*"  by  15  mils  thick, 
to  build  up  the  core.  If  thicker  material  is  employed  a  less  number  of 
sheets  will  be  needed.  Also  the  sheets  might  be  wider  as  shown  in  figure  7, 
page  22. 

WEIGHT  OF  THE  IRON  CORE. 

The  total  volume  of  the  iron  core  as  given  above  will  be  2*  x  2|  x  40  = 
275  cubic  inches.  The  mean  length  of  the  magnetic  circuit  is  40  inches. 
If  the  iron  weighs  0 . 27  pound  per  cubic  inch,  the  weight  of  the  core  is  275 
X  0.27  =  74  pounds. 


DESIGNING  THE   IRON    CIRCUIT. 

GORE  LOSSES. 

A  consideration  of  the  core  losses  from  the  application  of  the  results 
of  experimental  practice  will  be  in  order. 

The  total  volume,  in  cubic  inches,  of  the  iron  constituting  the  core  of  a 
transformer  is  found  by  multiplying  the  mean  length,  in  inches,  of  the 
magnetic  circuit,  by  its  cross  sectional  area,  in  square  inches.  The  volume 
of  the  core  will  be  expressed  by: 

V  =  AC?  (cubic  inches).  V  denoting  volume  in  cubic  inches;  Ac 
area  of  cross  section  of  iron  core  in  square  inches,  and  I  the  mean  length  of 
the  magnetic  circuit,  in  inches.  The  mean  length  of  the  magnetic  circuit 
shown  at  C  figure  7,  page  22  is  46  inches.  This  shows  holes  punched  in  the 
core  sheets  to  allow  bolts  to  be  passed  through,  to  bolt  the  sheets  firmly 
together. 


24  ,     Designing,  Making,  and  Operating  High-Pressure  Transformers 

The  eddy-current  loss  per  CUBIC  INCH  of  core,  when  made  of  thin 
plates,  as  found  by  careful  experimentation,  may  be  expressed  by: 

we  =  16.38  — rCr~     (12) 

in  which  equation,  We  denotes  watts,  b  denotes  the  thickness  of  the  iron 
plates,  IN  MILS;  that  is  in  thousandths  of  an  inch;  /  denotes  the  fre- 
quency of  the  primary  current,  and  necessarily  of  the  magnetic  flux  in  the 
iron  core;  33  denotes  the  flux  density,  in  gausses;  that  is  in  maxwells  per 
SQUARE  CENTIMETER.  The  flux  density  per  square  inch  in  the  pre- 
sent case  is  3000  X  6.45*  =  19350  maxwells.  Substituting  the  proper 
numerical  values  in  the  above  equation  gives : 

225   X  3600  X  9,000,000 
e   =  10,000,000,000,000,000 

1.638  X  2.25   X  3.6   X  9          119.4 

10,000  :  10,000 

=    .01194  WATT. 

DATA. 

b       =    T^TT  incn- 

=  15  mils. 

b2   =  225. 

/.=  60. 

/2  =  3600. 

33     =  3000  GAUSSES. 

332   =  9,000,000. 

It  may  be  noted  that  10  raised  to  the  16th.  power,  is  expressed  by 
writing  1  with  sixteen  ciphers  after  it.  Multiplying  10  by  itself  16  times 
will  prove  the  result. 

The  loss  per  cubic  inch  expressed  in  watts,  due  to  hysteresis,  may  be 
expressed  by : 

WH    =    — : ;  in  which  equation/and  33  have  the  samemean- 

107 

ing  as  previously;  (see  equation  (11)  page  18.)  while  K  denotes  a  so-called 
hysteretic  constant;  equal  to  about  0.0021  for  ordinary  thin  transformer- 
steel  sheets. 


*6.45  square  centimeters  equal  one  square  inch.     (See  page  3.) 


Designing,  Making,  and  Operating  High-Pressure  Transformers     25 

Substituting  the  proper  numerical  values  gives: 

16.38   X    .0021   X  60  X  3QQOi-6 
Wh   "  10,000,000 

1.638   X    .0021   X  6   X  3.65   =    .07533  WATT. 

f         DATA. 

K    =    .0021. 
/   =  60. 
_33     =  3000. 

log  931'6    =   1.6   X  log  3000. 
log  3000   =  3.477121 
1.6 


20862726 
3477121 

•   Therefore  logls1'6   =  5.5633936 
and   3000 r6   =  365000. 

The  total  CORE  LOSS  IN  WATTS  PER  CUBIC  INCH  is  therefore: 

We  +  Wh  =  0.01194  +  0.07533    =    .08721  watt. 

If  the  assumed  core  loss  is  to  be  25  watts  the  necessary  volume  of  iron 
will  be:  .nMuT  =  286  CUBIC  INCHES. 

This  is  the  minimum  allowable  volume  for  continuous  operation  at 
the  assumed  core  loss. 

It  may  be  noted  that  the  length  of  the  core  must  be  proper  to  accom- 
modate the  requisite  number  of  turns  of  wire,  both  primary  and  secondary, 
as  well  as  the  necessary  amount  of  insulating  material,  separating  the 
primary  from  the  secondary,  and  separating  the  sections  or  so-called 
"pies"  of  the  secondary  winding. 

The  so-called  "core  type"  of  transformer  is  always  adopted  for  high-     % 
pressure  work;  see  b,  figure  1,  page  5. 

To  obtain  an  idea  of  the  necessary  space  required  for  the  windings  ofc. 
the  transformer  being  designed,  again  consulting  the  table  on  page  21, 
the  diameter  of  No.  9  covered  wire,  (column  F)  being  .125  inch,  and  there 
being  300  turns,  the  cross  sectional  area  required  by  the  primary  windings 
is  0.125  X  0.125  X  300  =  4.68  square  inches. 

For  the  secondary  the  required  area  is  0.0169  X  0.0169  X  58650  = 
16f  square  inches. 

A  total  of  about  21  \  square  inches  is  required  for  both  windings.  If 
the  primary  is  wound  in  two  layers,  and  one  section  for  each  limb  of  the 


26     Designing,  Making,  and  Operating  High-Pressure  Transformers 

core,  the  necessary  length  of  core  to  accommodate  one  section  of  two  layers 
will  be  3ffi  X  0.125  =  9.4  inches.  The  distance  may  be  made  10 
inches  as  indicated  in  figure  6,  page  22. 

Allowing  50%  of  area  for  cross-section  of  insulation,  the  area  included 
by  the  core  will  need  to  be  about  42  square  inches.  If  the  opening  through 
the  core,  is  10  inches  in  one  direction,  the  other  dimension  of  the  opening 
(or  the  width)  will  need  to  be  4.2  inches.  This  should  be  taken  as  5 
inches,  when  building  the  core;  see  figure  6,  page  22. 

DIRECTIONS  AND  DATA  FOR  CONSTRUCTING  A  3  KILOWATT, 
20,000  VOLT  TRANSFORMER. 

The  following  directions  and  data  will  enable  anyone  to  construct  a 
transformer  for  use  on  a  60  cycle  alternating-current  circuit,  that  will  give 
an  output  of  about  3  kilowatts  continuously  without  overheating,  or  a  50% 
greater  output  for  short  intervals,  with  a  pressure  of  110  volts  applied  to 
its  primary,  while  delivering  the  output  at  about  20,000  volts. 

IRON  CORE. 

196  strips  of  soft  iron  (so-called  Russia  iron  that*  stove  pipe  is  made  of 
will  serve  well;  or  so-called  "transformer  steel"  may  be  used)  9£  inches 
long  by  2|  inches  wide,  and  196  strips  of  the  same  material  15^  inches  long 
by  2^  inches  wide;  all  ^V  °f  an  mch  thick. 

The  data  applying  to  the  iron  core  is  here  given  differently  than  that 
given  under  the  "Design  of  a  20,000  Volt  Transformer"  for  the  reason  that 
many  who  desire  to  construct  a  transformer  cannot  readily  obtain  the  thin 
"transformer  steel",  but  are  able  to  obtain  the  "Russia"  iron  from  local 
hardware  dealers.  This  iron  comes  usually  about  ^  of  an  inch  thick  in 
large'sheets,  from  which,  strips  of  the  desired  size  may  be  cut.  The  strip 
should  be  kept  as  flat  as  possible. 

1.  Carefully  remove  all  burrs  and  sharp  edges  from  the  iron  strips 
by  means  of  sand  paper  (No.  0),  or  by  means  of  a  fine  file. 

2.  Coat  both  sides  and  edges  of  each  strip  with  shellac  varnish. 

3.  Stand  strips  on  end  as  soon  as  varnished  and  allow  the  varnish 
to  dry  for  several  hours.     One  side  of  each  strip  may  be  varnished  and 
allowed  to  dry  thoroughly,  and  then  the  other  side  may  be  treated  likewise. 
The  drying  process  should  take  place  in  a  warm  dry  room. 

4.  Do  not  allow  one  freshly  varnished  strip  to  come  into  contact 
with  another  strip  while  drying. 

5.  While   the   strips  are  drying,   prepare  the   wooden  supporting 
structure  according  to  the  following: 


Designing,  Making,  and  Operating   High-Pressure  Transformers     27 

A  base  consisting  of  soft  pine,  made  of  planks  22  inches  long,  2  inches 
thick  and  of  sufficient  number  (depending  upon  their  width)  to  form  a  base 
22  inches  X  22  inches.  These  planks  to  be  cleated  together  by  screwing 
to  their  under  sides  two  cleats  of  the  same  material,  2  inches  thick,  22  inches 
long  and  4  inches  wide.  See  figure  8. 


Fig.  8. 


Fig.  9. 


Fig.  10. 


28     Designing,  Making,  and  Operating  High-Pressure  Transformers 


Fig.  11. 

The  lumber  used  should  be  planed  on  both  sides  and  edges. 

If  the  completed  transformer  is  to  be  moved  about,  from  one  place  to 
another,  very  frequently,  the  base  should  be  provided  with  heavy  casters, 
which  may  be  secured  to  the  under  surface  of  the  cleats.  "Feltoid" 
casters,  made  by  the  Burns  and  Bassick  Co.,  Bridgeport,  Conn.,  have  been 
found  to  give  the  best  satisfaction.  Four  of  these  are  sufficient:  one  for 
each  corner  of  the  base.  As  the  completed  transformer  weighs  about  140 
pounds  it  will  be  well  to  "block  up"  the  base  to  relieve  the  casters  of  the 
weight,  when  not  being  transported. 

6.  Provide  two  soft  pine  pieces,  each  19  inches  long,  1\  inches  wide, 
and  3  inches  high  as  indicated  at  M  and  M',  figure  8,  which  when  properly 
located  on  the  top  of  the  plank  base,  serve  to  provide  a  bearing  surface  for 
the  iron  core  of  the  transformer.     The  proper  position  for  the  bearing 
pieces  may  be  seen  by  consulting  figure  8,  page  27. 

7.  Bore  four  holes,*  two  of  which  are  indicated  by  h',  and  h",  T9^ 
inch  in  diameter,  completely  through  the  supporting  blocks,  M,  M',  the 
board  base  and  the  cleats.     The  distances  between  the  supporting  pieces 
and  between  the  centers  of  the  holes  are  given  in  figure  8. 

8.  Two  strips  of  hard  wood,  (oak  or  maple)  each  16  inches  long,  1\ 
inches  wide  and  1  inch  thick,  as  indicated  by  S,  and  S',  figure  9,  should  be 
provided  with  holes  to  coincide  with  those  in  the  supporting  blocks. 

*Care  should  be  taken  not  to  put  screws  in  the  cleats  and  base  where  it  is  necessary  to 
bore  the  holes. 


Designing,  Making,  and  Operating  High-Pressure  Transformers     29 

These  strips  serve  to  bind  the  iron  strips  firmly  together  by  means  of 
four  bolts,  12  inches  long  and  £  inch  in  diameter,  which  pass  down  on  either 
side  of  the  iron  core,  through  the  supporting  pieces,  and  the  base,  two  of 
which  are  shown  in  figure  9,  at  b  and  b'. 

9.  If  desired,  sand  paper  the  surfaces  of  the  wooden  structure,  and 
stain  with  cherry  or  oak  stain  as  preferred.     Apply  with  a  brush  a  "filler" 
consisting  of  £  pint  of  linseed  oil,  \  pint  turpentine  and  about  two  table- 
spoonfuls  of  corn  starch  thoroughly  mixed  together.     After  the  two  appli- 
cations have  dried  for  24  hours,  rub  the  surface  with  a  handful  of  excelsior, 
to  remove  lumps  and  excess  of  corn  starch,  and  apply  a  coat  of  shellac 
varnish.     After  this  has  dried  for  10  hours,  sand  paper  the  surface  with 
No.  00  sand  paper,  and  apply  a  second  coat  of  varnish.     Let  this  dry  for 
10  hours. 

10.  During  the  Periods  necessary  for  drying  processes,  the  work  of 
winding  the  coils  may  be  performed.     See  page  33. 

11.  Place  the  supporting  pieces  M  and  M'  in  position,  and  insert 
the  bolts  b  and  b'  in  M.     During  this  stage  of  the  construction  the  struc- 
ture should  be  supported  on  a  box  or  by  blocks  as  indicated  by  B  and  B', 
figure  10,  high  enough  to  allow  the  12  inch  bolts  to  be  inserted  from  below. 
The  bolts  may  be  inserted  from  the  top,  in  the  piece  M',  to  simply  hold  it 
temporarily  in  position. 

12.  Proceed  to  lay  the  iron  core  strips  in  position  as  shown  in  figure 
10.     Consult  figure  6,  page  22,  and  figure  7,  page  22.     The  two  long  strips 
a,  a',  should  be  parallel  with  each  other  and  at  right  angles  with  the  shorter 
end  strip,  e.     Directly  on  top  of  the  strips  already  laid  in  place,  apply 
another  layer  of  strips  as  indicated  in  figure  11,  page  28. 

Continue  piling  the  strips,  alternating  the  joints,  until  all  of  the  longer 
strips  and  one  half  of  the  shorter  strips  have  been  used. 

13.  Place  the  strip  S  in  position  and  bolt  down  firmly  by  means  of 
the  bolts  b  and  b'.     Just  before  the  final  turns  are  given* to  the  nuts  on 
b  and  b',  the  strips  may  be  carefully  lined  up,  by  means  of  a  small  block 
and  hammer,  or  by  using  a  wooden  mallet.     The  arrangement  now  ap- 
pears as  in  figure  9,  page  27. 

14.  If  now  the  structure  is  tipped  up  on  its  end,  n,  n',  figure  9,  the 
piece  M'  may  be  removed,  to  allow  the  primary  and  the  secondary  coils 
to  be  slipped  on  over  the  limbs  x  and  y  of  the  iron  core. 

It  is  very  essential  that  both  primary  and  secondary  coils  be  well 
insulated  from  the  connecting  end  yokes  of  the  iron  core.  This  may  be 
accomplished  by  building  up  an  insulating  sheet  using  the  scrap  pieces  of 
Empire  Cloth,  sticking  them  together  with  shellac  varnish,  and  com- 
pressing the  sheet  between  two  flat  boards  under  a  heavy  weight,  while 
the  shellac  varnish  hardens.  The  built  up  sheet  may  be  about  £  inch  thick 


30      Designing,  Making,  and  Operating  High-Pressure  Transformers 

shown  at  a,  figure  12,  page  31,  and  in  figure  14,  page  33;  also  in  position 
on  the  transformer  at  a,  figure  12.  A  sheet  in  the  process  of  construction 
is  shown  at  b,  figure  14,  and  a  finished  one  at  a,  same  figure.  Two  such 
sheets  are  needed  for  each  transformer,  as  shown  in  figure  16,  page  35. 

To  build  up  such  a  sheet,  place  a  square  piece  of  Empire  Cloth,  the 
desired  size,  on  a  flat  board,  and  apply  a  coat  of  shellac  varnish  to  its  upper 
surface.  Immediately  place  scrap  pieces  of  the  cloth  on  the  varnished 
surface  and  apply  a  coat  of  varnish  to  their  upper  surface.  Continue  this 
process  until  the  desired  thickness  is  attained.  Place  another  whole  sheet 
of  Empire  Cloth  over  the  top  of  the  built  up  sheet,  place  a  flat  board  on  the 
completed  built  up  sheet,  and  apply  a  weight  of  about  50  or  75  pounds. 
Allow  the  sheet  to  dry  for  twenty-four  hours  and  then  trim  to  the  desired 
shape,  with  a  sharp  knife.  By  this  process  there  is  no  waste  of  Empire 
Cloth,  and  a  sheet  of  material  having  insulating  qualities  approaching 
those  of  mica  is  obtained  at  a  small  cost. 

15.  Slip  each  tube,  containing  each  section  of  the  "primary"  wind- 
ings, over  each  leg  of  the  core,  bending  the  terminals  to  allow  the  tubes 
separating  the  primary  from  the  secondary  windings  to  be  slipped  over 
the  primary  coils,  after  adjusting  one  of  the  insulating  discs  to  the  lower 
end  of  each  separating  tube,  about  2  inches  from  the  end. 

An  excellent  insulating  separating  tube  may  be  constructed  or  "built 
up"  by  first  gluing  two  layers  of  cardboard  to  form  a  tube  of  sufficient 
size  to  slip  over  the  primary  windings  easily;  applying  a  coat  of  shellac 
varnish  to  the  outer  surface,  and  immediately  winding  thereon  in  a  spiral 
fashion,  strips  of  Empire  Cloth,  about  1  inch  wide,  and  about  5  feet  in 
length.  The  winding  should  lap  each  other  about  |  inch,  and  after  one 
complete  winding  has  been  finished,  its  surface  may  be  coated  with  shellac 
varnish  and  another  spiral  wound  on.  The  process  may  be  continued 
until  a  tube  qf  the  proper  thickness  has  been  built  up.  After  such  a  tube 
has  been  allowed  to  thoroughly  dry,  a  strong  tube  having  excellent  insulating 
qualities  is  the  result. 

The  outside  diameter  of  this  separating  tube  should  be  slightly  less 
than  the  inside  diameter  of  the  secondary  pies. 

These  separating  tubes  are  shown  at  t,  t',  figure  12,  page  31. 

16.  Next  slip  on  over  the  separating  tube  a  pair  of  "pies"  of  the 
secondary  winding,  being  arranged  as  explained  under  winding  of  secondary 
coils,  page  33,  until  they  rest  against  the  end  insulating  disc. 

17.  Proceed  to  add  the  secondary  "pies",  to  both  limbs  of  the  trans- 
former putting  16  single  pies  or  8  "units"  on  each  limb.     The  units  should 
be  placed  so  that  their  terminals  are  all  on  the  same  line,  to  facilitate  in 
joining  them  together. 


Designing,  Making,  and  Operating   High-Pressure  Transformers      31 


Fig.  12. 

18.  The  units  or  pairs  of  pies  should  be  placed  relatively  with  each 
other  so  that  when  their  terminals  are  connected  with  each  other  there 
will  be  a  continuous  winding,  in  the  same  direction,  from  one  end  of  each 
limb  to  the  other  end  of  the  same  limb.     That  is,  so  that  each  half  of  the 
secondary  winding  shall  consist  of  turns  of  wire  all  in  the  same  direction 
of  winding,  and  the  two  half  sections  of  the  complete  secondary  must  be 
so  connected  with  each  other  as  to  work  properly  together  and  not  in 
"opposition". 

Figure  3,  page  12,  will  give  an  idea  of  the  relation  of  the  turns  in  the 
windings. 

19.  The  free  ends  of  the  "units"  should  be  carefully  cleaned,  twisted 
together,  and  soldered  by  use  of  a  small  soldering  iron.     Do  not  use  a  lamp 
in  soldering  small  wires.     The  heat  of  the  flame  tends  to  "burn"  the  wire, 
making  a  very  poor  joint  and  doing  permanent  injury  to  the  wire. 

20.  Properly  connect  the  half -sections  of  the  secondary  with  each 
other  and  bring  the  two  end  terminals  to  the  top  of  hard  rubber  posts 
each  ^  inch  in  diameter,  3  inches  high,  located  as  shown  in  figure  16,  page  35. 
These  hard  rubber  posts  may  be  inserted  in  \  inch  holes  about  1  inch  deep. 

21 .  The  primary  terminals  may  have  flexible  leads,  soldered  to  them 
and  brought  out  to  four  binding-posts,  to  allow  various  arrangements  of 
connections.     See  figure  12. 

WINDING  THE  PRIMARY  COILS. 

The  primary  windings  require  18  pounds  of  No.  12  Double  cotton 
covered  (D.  C.  C.)  B.  &  S.  gauge,  copper  wire,  wound  double,  two  wires 
being  wound  side  by  side  to  form  two  layers,  one  having  40  turns,  the  other 


32     Designing,  Making,  and  Operating  High-Pressure  Transformers 

having  60  turns,  per  section  or  per  limb  of  the  transformer.  The  total 
operative  primary  turns  are  therefore  (40  +  60)  x  2  =  200  TURNS. 
In  reality  there  are  400  turns  of  wire;  two  sets  of  200  turns  each.  The 
two  sets  connected  together  in  parallel  constitute  the  200  operative  turns. 
This  shows  how  an  equivalent  number  of  smaller  wires  may  act  as  one  large 
wire,  and  also  renders  winding  much  easier;  the  two  smaller  wires  being 
much  more  flexible  than  the  equivalent  single  wire. 

The  primary  in  one  transformer  was  wound  directly  on  the  iron  core,  as 
shown  in  figure  12,  being  insulated  from  the  iron  core  by  several  layers  of 
"Empire  Cloth";  having  a  thickness  of  about  ^  of  an  inch.  It  might  have 
been  wound  on  a  form  such  as  shown  in  figure  13,  taken  from  the  form,  and 


Fig.  13. 

slipped  on  over  the  limb  of  the  core.  If  wound  in  circular  form,  it  allows 
the  air  to  circulate  through  the  spaces  between  the  coil  and  the  core,  tend- 
ing to  keep  the  temperature  of  the  transformer,  when  in  operation,  at  a 
low  value.  This  however  requires  a  greater  length  of  wire.  The  arrange- 
ment of  the  winding  form  should  be  noted.  The  cylinder  is  mounted  to  be 
turned  by  the  handle  h,  is  provided  with  a  speed-counter  at  i,  for  register- 
ing the  number  of  turns,  and  has  a  diagonal  cut  cc'  through  it,  so  that  its 
thinner  ends  may  be  screwed  (screw  at  S)  to  the  thicker  ends  thus  holding 
the  sections  together.  After  a  coil  is  wound,  the  screws  at  the  ends  may 
be  removed,  allowing  the  form  to  be  easily  withdrawn  from  the  coil.  The 
end  bearing  e  and  the  handle  h  are  removed  by  removing  screws. 


Designing ,  Making,  and  Operating  High-Pressure  Transformers     33 

DIRECTIONS  FOR  WINDING  THE  SECONDARY  COILS. 

The  secondary  of  the  transformer  requires  20  pounds  of  No.  26*;B.  & 
S.  gauge,  double  cotton  covered  copper  magnet  wire. 


Fig.   14. 

This  secondary  is  wound  in  "pies"  or  thin  sections  shown  at  e  and  f 
figure  14,  4^  inches,  internal  diameter,  6|  inches  over  all  diameter,  and 
inch  thick.  Each  pie  is  first  wound  on  a  form  as  shown  in  figure  15, 

carefully  bound  together  with  pieces  of 
the  No.  26  wire,  to  enable  it  to  be  re- 
moved from  the  winding  form,  and  then 
soaked  in  melted  paraffin,  in  a  proper 
sized  dish.  When  removed  from  the 
melted  paraffin,  and  allowed  to  cool, 
the  pie  may  be  easily  manipulated. 
Each  pie  should  contain  800  turns  of 
the  No.  26  wire,  and  32  pies  are  needed 
for  the  finished  transformer,  if  20,000 
volts  are  to  be  obtained.  A  set  of  fin- 
ished pies  is  shown  in  process  of  being 
assembled  on  the  separating  tube,  at  e 
15  and  e',  figure  12,  page  31. 


r.E-A, 


34      Designing,  Making,  and  Operating   High-Pressure  Transformers 

The  winding  will  be  greatly  facilitated  if  done  in  a  lathe. 

A  proper  tension  should  be  maintained  on  the  wire  while  winding  it 
and  the  wire  should  be  continually  guided  from  one  side  of  the  form  to  the 
other  while  winding,  to  prevent  humps  in  the  winding,  or  the  slipping  down 
of  a  turn  between  the  turns  already  wound,  and  the  side  of  the  form. 

It  should  be  noted  that  the  tension  on  the  wire  while  it  is  being  wound* 
determines  whether  the  number  of  turns  stated  may  be  wound  in  the  given 
space.  It  is  not  considered  advisable  to  wind  the  pies  too  tightly  as  this 
does  not  allow  the  hot  paraffin  to  soak  into  their  interior. 

A  tube,  t,  figure  12,  page  31,  made  of  about  10  layers  of  Empire  Cloth 
separates  the  primary  from  the  secondary  windings;  while  each  secondary 
pie  is  separated  from  its  neighbor  by  five  discs  put  side  by  side  to  form  an 
insulating  separator  about  TV  inch  thick,  shown  at  c,  figure  14,  page  33 
and  in  figure  12,  page  31,  cut  from  a  sheet  of  the  Empire  Cloth.  These 
discs  are  cut  to  fit  closely  to  the  tube  separating  the  primary  and  second- 
ary, and  having  an  outside  diameter  about  one  inch  larger  than  the  over 
all  diameter  of  the  secondary  pies.  The  over  all  diameter  of  the  separating 
discs  may  be  8  inches.  A  card  board  pattern  used  in  cutting  out  the 
separating  discs  is  shown  at  d,  figure  14.  If  the  transformer  is  to  be 
immersed  in  oil,  ordinary  card  board  may  be  used  in  place  of  the  Empire 
Cloth. 

APPROXIMATE  COST  OF  MATERIALS. 

The  following  is  an  itemized  account  showing  the  approximate  cost 
of  the  transformer  just  described. 

Wood  for  base $  1 . 00 

Casters 1 .34 

4  bolts,  12"  x  \" 20 

Iron  strips  for  core,  82£  Ibs 9 .00 

Wire  for  primary,  18  Ibs.,  No.  12 3.00 

Wire  for  secondary,  20  Ibs.,  No.  26 10.00 

Linseed  oil,  turpentine,  and  shellac 1 . 00 

Paraffin  wax 1 . 20 

Binding  posts ,  .40 

10  yards  of  Empire  Cloth 4.00 

$31.14 


Designing,  Making,  and  Operating  High-Pressure  Transformers     35 

The  completed  transformer  is  shown  in  figure  16,  the  secondary  spark 
gap  being  made  of  copper  wire  bent  into  the  shape  of  horns,  arranged  on 
sliding  brass  rods,  supported  by  hard  rubber  posts.  Flexible  "drop  cord" 
wires  are  used  for  primary  connections. 

The  purchase  price  of  a  transformer  such  as  the  one  described,  would 
probably  be  not  less  than  SI 00. 00. 


Fig.   16. 


OIL  IMMERSED  TRANSFORMERS. 

All  high-pressure  transformers  will  operate  much  more  satisfactorily 
if  surrounded  with  oil,  such  as  paraffin  oil,  which  belongs  to  the  kerosene 
family.  The  oil  is  a  liquid  insulator  that  is  self  mending  after  a  spark 
discharges  through  it,  and  acts  to  convey  the  heat  away  from  the  hottest 
portions  of  the  transformer;  preventing  excessive  heating. 

Good  insulating  oil  called  "transil"  or  transformer  oil  may  be  pur- 
chased for  about  50  cents  per  gallon. 

To  make  an  oil  containing  tank  for  a  transformer,  construct  a  box 
using  soft  pine  boards  about  f-  inch  thick,  large  enough  to  allow  the  com- 
pleted transformer  to  be  inserted  with  an  all  around  clearance  of  about  1 
inch.  Cover  the  outside  of  the  box  with  thin  sheet  copper  or  ordinary 
"roofing"  tin,  carefully  soldering  all  joints  to  prevent  leaking  of  oil.  A 
faucet  may  be  soldered  to  one  side  near  the  bottom  of  the  box  to  allow  the 


36     Designing,  Making,  and  Operating   High-Pressure  Transformers 

oil  to  be  drawn  off  when  desirable.  The  oil  may  however  be  syphoned 
from  the  box  when  necessary,  by  means  of  a  flexible  rubber  tube  or  hose, 
doing  away  with  a  faucet,  and  preventing  loss  of  oil  by  accidental  opening 
of  a  faucet. 

If  oil  is  employed  as  an  insulator,  cheaper  separating  insulation  may 
be  used,  and  much  labor  saved  in  constructing  a  transformer,  as  there  will 
then  be  no  need  of  soaking  coils  in  melted  paraffin. 

A  word  of  caution  may  be  valuable  regarding  the  first  trial  of  the 
completed  oil  immersed  transformer.  Never  attempt  to  operate  a  high- 
pressure  oil  immersed  transformer,  for  at  least  24  hours  after  being  placed 
in  the  oil.  It  requires  time  for  the  oil  to  completely  soak  into  the  interior 
of  coils  which  contain  many  turns  of  wire. 

PRECAUTIONS. 

All  material  used  in  the  construction  of  high  pressure  transformers 
should  be  carefully  inspected  for  defects.  The  greatest  care  should  be 
exercised  in  the  various  processes  of  construction  to  obtain  the  best  pos- 
sible insulation  of  the  various  portions,  the  iron  plates  of  the  core,  and  the 
windings.  The  insulation  of  the  different  portions  from  one  another  may 
be  tested  by  use  of  a  telephone  receiver  and  a  single  dry  cell. 

The  several  coils  should  be  individually  tested  to  determine  any  broken 
wire  that  may  exist. 

All  coils  should  be  carefully  inspected  and  tested  individually  before 
assembling. 

Never  use  enameled  wire  in  high-pressure  transformer  construction. 

Particular  care  in  insulating  is  necessary,  since  it  is  the  maximum  value 
of  an  alternating-pressure  that  tends  to  puncture  and  break  down  insula- 
tion. 

For  example,  if  the  pressure  wave  is  a  sine-wave  having  a  working 
value  (effective)  of  20,000  volts,  the  maximum  value  of  this  pressure  is 
20,000  x  1 .414;  which  is  28,280  VOLTS. 

The  maximum  value  of  a  sine-curve  is  equal  to  the  |/2  (square  root 
of  2  =  1 . 414)  times  its  effective  value. 

CAUTIONS. 

The  experimenter  using  high-pressure  apparatus  that  is  connected 
with  service  mains,  should  keep  in  mind  that  the  source  of  energy  is  capable 
of  supplying  a  considerable  amount;  meaning  that  personal  contact  with 
the  high  pressure  side  of  the  apparatus  does  not  cause  the  input  to  the 
apparatus  (and  to  the  individual)  to  cease.  The  discharge  of  a  Leyden  jar 
or  of  a  condenser  through  the  body  does  not  prove  fatal,  because'the  supply 


Designing,  Making,  and  Operating  High-Pressure  Transformers     37 

of  energy  is  not  only  limited,  but  is  very  quickly  exhausted;  so  quickly  in 
fact  that  the  effect  is  not  perhaps  even  harmful.  The  pressure  in  such  a 
case  may  be  much  greater  than  that  produced  by  an  apparatus,  which 
furnishing  a  much  lower  pressure  continuously,  is  dangerous.  Contact 
with  the  high-pressure  terminals  of  a  transformer  should  be  guarded  against' 
The  ordinary  frequencies  offer  no  protection  to  the  individual.  A  CON- 
TINUOUS CURRENT  OF  ^  (.03)  OF  AN  AMPERE,  IN  A  VITAL 
ORGAN,  IS  FATAL. 

Even  though  the  resistance  of  contact  through  the  two  hands  may  be 
50,000  ohms,  it  is  evident  that  20,000  volts  will  send  a  current  of  f  #  J#$ 
=  f  of  an  ampere  through  the  body: — enough  to  kill  a  person  several  times. 

Always  disconnect  the  double  pole  knife  switch,  connected  with  the 
primary,  before  touching  any  part  of  the  secondary,  with  even  one  hand  or 
with  a  stick. 

The  secondary  should  be  provided  with  fuses  of  small  current  capacity 
in  addition  to  the  primary  fuses. 

In  case  of  accidental  short-circuit  of  the  secondary,  or  in  case  of  ac- 
cidental contact  with  the  secondary,  the  small  secondary  fuses  will  blow 
out  very  quickly,  offering  better  protection  than  offered  by  the  larger 
primary  fuses. 

Never  attempt  to  adjust  a  high  pressure  wire  with  a  screw  driver, 
with  the  apparatus  operating. 


Fig.   17. 


38     Designing,  Making,  and  Operating  High-Pressure  Transformers 

DATA  APPLYING  TO  A  4,000  VOLT  TRANSFORMER. 

A  1  K.  W.  transformer  to  transform  from  110  volts  at  60  cycles,  to 
about  4,000  volts,  is  shown,  in  the  process  of  construction  in  figures  17, 
and  18,  pages  37  and  38.  The  ratio  of  transformation  is  36 . 3. 


Fig.  18. 

The  core  consists  of  angle  strips  of  Russia  iron,  2|  inches  wide,  bolted 
together  as  shown  at  b,  figure  17,  page  37  and  in  figure  18,  to  make  a 
thickness  of  core  of  1\  inches.  The  angle  strips 
are  cut  from  the  sheet  of  iron  as  indicated  in 
figure  19,  to  minimize  waste  of  material.  The 
longer  leg  of  the  larger  angle  piece  is  10|  inches, 
and  the  shorter  leg  is  7f  inches  long  or  13|  inches 
and  10|  inches  over  all.  This  method  of  con- 
struction allows  only  two  magnetic  joints,  and 
facilitates  the  taking  apart  of  the  device  and 
the  removal  of  the  coils.  One  section  of  the  core 
is  shown  at  C,  figure  17,  page  37.  The  complete 
iron  core  weighs  about  55  pounds.  The  primary 
consists  of  two  coils,  of  No.  9  B.  &  S.  gauge 
D.  C.  C.  copper  magnet  wire,  P  and  P',  figure  17, 
Fig.  19.  page  37,  each  wound  in  two  layers,  61  turns,  per 


Designing ',  Making,  and  Operating  High- Pressure  Transformers     39 

layer,  making  a  total  of  244  primary  turns,  all  weighing  about  9  pounds. 
The  primary  was  wound  on  the  winding  form  shown  in  figure  13,  page  32, 
the  form  being  4  inches  in  diameter.  Two  layers  of  ordinary  card  board 
were  first  wound  on  the  form  and  glued  together,  the  wire  being  then  wound 
on  over  the  cardboard,  tied  together  with  tape,  and  the  winding  form  re- 
moved. The  inner  diameter  of  the  primary  coils  was  4^  inches,  and  the 
over  all  diameter,  4f  inches.  The  coils  were  given  three  coats  of  shellac 
varnish. 

The  secondary  consists  of  eight  coils  of  No.  26  B.  &  S.  gauge,  D.  C.  C. 
copper  magnet  wire,  wound  on  wooden*  spools  as  shown  at  S  in  figure  17, 
page  37,  and  at  S,  S',  figure  18;  each  spool  containing  about  1,100  turns  of 
wire.  As  can  be  noticed  in  figure  17  and  in  figure  18  the  wire  was  very 


Fig.  20. 

carefully  wound,  in  even  layers,  which  renders  it  possible  to  wind  more 
turns  in  any  given  space.  This  transformer  was  designed  for  use  without 
oil  immersion,  and  without  soaking  the  secondary  coils  in  melted  paraffin; 
being  simply  varnished  over  with  shellac  varnish. 

*Dry  soft  pine  is  the  best  wood  to  use;  dry  white- wood  being  the'next  in  desirability. 


40      Designing,  Making,  and  Operating  High-Pressure  Transformers 

The  spools  for  the  secondary  were  turned  out  in  a  wood-turning  lathe, 
and  had  the  following  dimensions: — 

Over  all,  6|  inches.  Width  over  all,  1||  inches. 

Inner  hole,  4|£  inches.  Width  of  winding  space,  1§  inches. 

Depth  of  winding  space,  lf\  inches. 

The  wooden  spools  were  thoroughly  soaked  in  hot  paraffin  and  cooled 
before  the  secondary  was  wound  onto  them.  The  application  of  two  coats 
of  shellac  varnish  would  answer  in  place  of  paraffin. 

Figure  18  shows  one  spool  S",  wound  with  wire,  and  seven  empty 
spools.  Figure  20  shows  an  arrangement  for  winding  the  wire  on  to  a 
spool  f  by  means  of  the  handle  h. 

The  spools  are  so  wound  that  two  may  be  placed  adjacent  to  each 
other,  the  inner  ends  of  the  windings  on  the  two  spools  coming  together, 
so  that  when  joined  the  two  spools  constitute  one  unit,  of  continuous  wind- 
ing in  the  same  direction.  This  allows  the  inner  ends  and  the  outer  ends 
of  wires  from  two  units  (or  all  the  units)  to  be  directly  joined  together, 
constituting  a  continuous  winding,  in  the  same  direction,  if  any  number 
of  units  are  connected  together. 

If  taps  are  brought  out  from  any  single  spool,  a  pressure  of  %  the  total, 
or  about  500  volts  may  be  obtained.  One  unit,  two  spools  will  give  about 
1000  volts. 

Values  of  pressure  of  500,  1000,  1500,.  2000,  2500,  3000,  3500  and  4000 
volts  may  be  obtained  by  making  taps  to  proper  points. 

POSSIBILITIES    OF    A    TRANSFORMER    AS    A    FREQUENCY 

CHANGER. 

All  alternating-current  waves  are  not  true  "SINE-CURVE"  waves. 
When  not  sine-curve  waves  they  are  made  up  of  the  sum  of  a  number  of 
sine-curves,  having  different  amplitudes  and  different  frequencies  from  that 
of  the  so-called  fundamental  or  resultant  curve. 

Figure  21  shows  an  alternating-wave: — either  an  alterating-pressure 
or  an  alternating-current — that  is  made  up  of  the  sum  of  three  sine-waves. 
Each  point,  (designated  by  being  surrounded  with  a  small  circle)  on  the 
fundamental  or  resultant  curve  was  located  by  adding,  algebraically  the 
corresponding  vertical  heights  of  the  three  component  sine-curves. 

Irregular  shaped  alternating-curves  found  in  practice  are  made  up  of 
sine-waves  having  frequencies  that  are  an  odd  number  of  times  the  fre- 
quency of  their  fundamental.  An  alternating-current  wave  having  a 
frequency  of  60  cycles  per  second,  may  be  made  up  of  four  separate  sine- 
waves,  having  frequencies  of  1,  3,  5,  and  7  times  60:  namely,  60,  180,  300 


Designing,  Making,  and  Operating   High-Pressure  Transformers      41 


42      Designing,  Making,  and  Operating  High-Pressure  Transformers 

and  420  cycles  respectively  per  second.  By  low  values  of  magnetic 
flux  in  the  iron  core  of  a  transformer,  by  a  small  primary  current,  one  of  the 
component  frequencies  of  the  fundamental  may  be  brought  into  promi- 
nence, and  thus  the  transformer,  in  a  degree,  can  be  made  to  act  as  a  fre- 
quency changer;  the  changes  of  course  being  limited  in  number.  Many 
current-curves  in  practice  have  been  found  to  consist  of  as  many  as  27 
component  sine-curves,  the  frequency  of  each  being  an  "odd"  number  of 
times  that  of  the  fundamental. 

Transformers  arranged  on  three-phase  circuits  may  be  well  adapted 
for  frequency  changers,  acting  on  the  principle  of  magnetic  supersaturation. 
The  "efficiency"  of  frequency  changers  based  upon  the  foregoing  principle 
will  not  be  high. 

HOW  TO  OBTAIN  UNITY  POWER  FACTOR. 

It  is  undesirable  that  any  alternating-current  device  should  operate 
at  a  low  power  factor,  since  this  condition  means  increased  losses,  a  greater 
first  cost,  and  an  attendant  increased  operating  expense. 

Any  method  of  keeping  the  power  factor  at  a  high  value,  (the  greatest 
value  being  unity)  is  valuable  so  far  as  increase  in  operating  efficiency  is 
concerned. 

A  "condenser"  connected  with  any  coil  which  has  inductance,  will  tend 
to  increase  the  power  factor,  and  if  the  proper  numerical  relation  exists 
between  the  "capacity"  of  the  condenser  and  the  coefficient  of  inductance 
of  the  coil,  a  power  factor  of  unity  may  be  expressed  by: 

27T/C    =  — 7—;  (13)  from  which  may  be  obtained: 

27T/L 

C   =  — 272"-     Here  C  denotes  the  capacity  of  a  condenser,   ex- 
4?r  j   JL 

pressed  in  farads:  f  denotes  the  frequency  of  the  applied  pressure;  L  de- 
notes the  coefficient  of  inductance,  expressed  in  henry s,  and  TT  as  usual, 
denotes  the  number  3 . 1416.  See  page  3. 

It  should  be  observed  that  the  larger  the  value  of  L  the  less  the  re- 
quired value  of  C,  to  produce  unity  power  factor  at  any  fixed  frequency. 
This  means  that  for  a  large  coil  of  many  turns  with  a  large  iron  core,  a 
condenser  having  a  small  capacity  is  needed  to  produce  a  power  factor  of 
unity.  A  condenser  connected  in  series  or  in  parallel  with  the  primary  of 
a  transformer,  improves  the  power  factor. 

Likewise  a  condenser  connected  with  the  secondary  improves  the  power 
factor  of  the  secondary,  and  greatly  increases  the  sparking  ability  of  high- 
pressure  transformers. 


Designing,  Making,  and  Operating   High-Pressure  Transformers     43 

A  condenser  used  in  connection  with  the  high-pressure  secondary  has 
a  much  smaller  capacity,  and  is  constructed  differently  from  a  condenser 
which  is  to  be  connected  with  the  low  pressure  primary.  Any  condenser 
that  is  to  be  used  with  high  pressures  must  be  made  of  thick  metal  plates, 
very  carefully  insulated  with  thick  glass  plates,  and  immersed  in  oil;  while 
a  condenser  for  low  pressures  may  be  made  of  ordinary  tin  foil,  separated 
by  thin  paraffined  paper. 

The  following  numerical  example  will  be  given:  TO  FIND  THE 
CAPACITY  OF  A  CONDENSER  THAT  WILL  NEUTRALIZE  THE 
INDUCTANCE  OF  THE  PRIMARY  COIL  OF  A  TRANSFORMER 
WHOSE  COEFFICIENT  OF  INDUCTANCE  L  =  i  HENRY,  IF  THE 
FREQUENCY  OF  THE  APPLIED  PRESSURE  IS  60  CYCLES  PER 
SECOND. 

Making  the  proper  numerical  substitutions  in  equation  (13),  page  42 
gives: 

nnrwwnQAO 

.0000070362 


C   = 


0000070362 


2  X 


=    .0000140724  farad. 


which  is  equal  to 


0000140724 
1000000 


=    14. 072  microfarads. 
(One  farad  is  equal  to  1000000  microfarads) 


f 
L 


DATA. 

3.14159 
9.8696 
60  cycles. 
3600 
\  henry. 


=  .0000070362 


Next  suppose  the  inductance  of  the  secondary  of  the  above  transformer 
is  50  henrys;  find  the  numerical  value  of  the  capacity  of  a  condenser  to  give 
a  unity  power  factor. 

In  this  case: 


.0000070362 
50 


=    .00000014072  farad:  or 


. 00000014072   =  0.1407  MICROFARAD. 
1000000 

The  greater  inductance  of  the  high-pressure  circuit  of  a  transformer 
is  because  of  the  greater  number  of  turns  of  wire  constituting  this  circuit. 


44      Designing,  Making,  and  Operating   High-Pressure  Transformers 

Inductance  varies  directly  as  the  square  of  the  number  of  turns  on  any  given 
coil.  Doubling  the  number  of  turns  increases  the  inductance  fourfold. 

Another  term  for  unity  power  factor  is  "resonance". 

One  of  a  number  of  odd  harmonics  may  be  rendered  prominent  by 
connecting  a  condenser  (in  series)  with  the  secondary  of  a  transformer  and 
producing  "resonance"  with  an  odd  harmonic  instead  of  with  the  funda- 
mental itself. 

Applying  the  foregoing  principle,  the  value  of  a  capacity  that  will 
produce  resonance  with  the  third  harmonic  frequency  may  be  found.  If 
the  applied  pressure  has  a  frequency  of  60  its  third  harmonic  is  3  x  60  = 
180  cycles  per  second.  In  this  case: 


C3 


47r2  x  ISO2  x   i         39.478  x  32400  x  i 

= =    .00000156  farad. 

1279100 

=     1.56  MICROFARAD. 

/ 

A  condenser  having  this  capacity,  connected  with  the  primary,  would 
tend  to  bring  the  third  harmonic  frequency  into  prominence,  causing  the 
arrangement  to  act  as  a  frequency  changer,  from  60  to  180. 

The  value  of  a  capacity  to  reinforce  the  f.fth  harmonic  would  be : 

C5   =   1         =  0.562  MICROFARAD. 

39.478   x  3002  x  \ 

A  condenser  having  this  capacity  will  tend  to  make  prominent  a  fre- 
quency of  300  cycles  per  second.  By  using  a  variable  condenser  properly 
graduated,  the  different  odd  harmonics  may  be  rendered  prominent.  For 
this  particular  primary  a  condenser  having  a  capacity  of  0.3  microfarad 
will  bring  out  the  seventh  harmonic. 

METHODS  OF  CONNECTING  PRIMARY  COILS  TO  PRODUCE 
DIFFERENT  SECONDARY  PRESSURES. 

The  induced  secondary  pressure  in  any  transformer  depends  upon  the 
magnitude  of  the  applied  primary  pressure. 

If  pressure  is  used  that  is  supplied  from  so-called  constant  pressure 
mains,  it  is  impossible,  with  a  coil  having  a  single  winding,  to  increase  the 
induced  secondary  pressure;  it  may  however  be  readily  reduced  by  connect- 
ing resistance,  (either  inductive  or  non-inductive)  in  series  with  the  single 
coil. 


Designing,  Making,  and  Operating   High-Pressure  Transformers      45 

With  two  primary  coils,  on  the  other  hand,  a  method  for  varying  the 
secondary  pressure  may  be  employed,  by  first  connecting  the  two  primary 
coils  in  series.  The  two  coils  may  next  be  connected  together  in  parallel, 
with  resistance  in  series  with  the  parallel  arrangement  of  the  two  coils. 
By  varying  the  amount  of  the  resistance,  the  applied  pressure  may  be 
varied  as  desired. 

If  the  applied  primary  pressure  is  110  volts,  and  the  two  primary  coils 
are  connected  in  series,  the  pressure  applied  to  each  coil  is  55  volts.  When 
the  two  coils  are  connected  with  110  volt  mains,  each  coil  receives  an  ap- 
plied pressure  of  110  volts  instead  of  only  55  as  when  the  coils  were  in 
series.  Much  more  current  in  the  coils  is  the  result,  according  to  equation 
(1),  page  7,  and  the  flux  density  in  the  iron  core  is  greatly  increased  ac- 
cording to  equation  (11),  page  18. 

Another  way  of  expressing  the  matter  would  be  based  upon  the  con- 
dition that  the  pressure  per  turn  of  both  primary  and  secondary  is  the  same. 
If  the  pressure  per  turn  of  the  primary  is  increased,  then  the  pressure  per 
turn  of  the  secondary  is  also  increased. 

EXAMPLE.  Suppose  the  primary  of  a  transformer  consists  of  two 
coils,  each  having  110  turns  of  wire,  while  the  secondary  of  the  same  trans- 
former consists  of  two  sections  or  coils,  each  having  2200  turns. 

If  the  two  primary  coils  are  connected  in  series  and  110  volts  applied, 
the  primary  per  turn  pressure  will  be  A4§  =  k  volt.  If  the  per  turn  pres- 
sure of  the  secondary  is  also  £  volt,  the  secondary  terminal  pressure  will  be 
2200  volts,  provided  the  secondary  coils  are  also  connected  in  series.  If 
the  secondary  coils  in  this  case  should  be  connected  in  parallel,  the  secon- 
dary terminal  pressure  would  of  course  be  1100  volts. 

Now  assume  that  110  volts  is  applied  to  each  individual  primary  coil; 
the  two  coils  being  in  parallel.  The  per  turn  pressure  will  be  one  volt.  The 
induced  secondary  pressure  will  be  1  volt  per  turn;  giving  a  secondary 
terminal  pressure  of  4400  volts  if  the  two  secondary  coils  are  in  series,  and 
2200  if  they  are  in  parallel. 

With  the  latter  arrangement,  care  will  need  be  taken  that  the  coils  are 
not  overheated. 

If  two  similar  transformers  have  their  primarys  connected  with  the 
same  supply  mains,  and  their  secondaries  connected  in  series  with  each 
other  the  combined  terminal  pressures  will  be  double  that  of  a  single  trans- 
former. If  ten  transformers,  each  giving  a  secondary  terminal  pressure  of 
100,000  volts,  have  their  primaries  all  connected  together  in  parallel  and  to 
the  same  service  mains,  while  their  secondaries  are  all  properly  connected 
together  in  series,  the  combined  terminal  pressure  would  be  1,000,000  volts, 
which  would  produce  a  vigorous  spark. 


46     Designing,  Making,  and  Operating   High-Pressure  Transformers 

PRICE  OF  MATERIALS  FOR  BUILDING  THE  HIGH  PRESSURE 

TRANSFORMER  DESCRIBED  ON  PAGE  26  OF  THIS  BOOK, 

AND    FOR    BUILDING    THE    TRANSFORMER    AS    PER 

PAGE  38. 

Iron  strip  for  Core 20  cts  per  pound. 

Wire  for  Primary 25  cts  per  pound. 

Wire  for  Secondary 35  cts  per  pound. 

Bolts  and  Screws 30  cents. 

Paraffin  Wax 15  cts  per  pound. 

Binding  Posts 15   cts.   each. 

Empire  Cloth 40   cts.  per  yard. 

Prices  subject  to  change  without  notice.     Remit  amount  with  order  to 

ENGINEERING  EDUCATION  EXTENSION, 
BOX  41.  HANOVER,  N.  H. 


How  To  Make  Low  Pressure  Transformers 

ILLUSTRATED.    SECOND  EDITION  with  Additions 


Many  transformers  have  been  successfully  built  according  to  the 
suggestions  and  directions  given  in  this  small  book. 

The  results  have  been  most  gratifying  to  the  author,  who  has  had 
the  pleasure  of  testing  the  efficiency  of  many  of  the  small  experimental 
transformers  built  by  "Young  America,"  following  the  printed  di- 
rections. 

The  completed  transformers  have  been  a  source  of  instructive 
amusement  for  those  who  delight  in  electrical  experiments ;  since,  they 
may  be  employed  to  operate  small  arc  lights,  small  direct-current 
series  motors  on  toy  electric  railways,  and  many  other  applications. 

The  most  popular  book  for  amateurs  ever  published.  Used  by 
Technical  and  Industrial  High  Schools. 

From  Railway  Age   Gazette,   November,   1915 : 

How  to  Make  Low  Pressure   Transformers.     By    Prof.   F.   F.   Austin, 
Hanover,  N.  H.     17  pages,  4  illustrations,  4-)4  i"-  by  7^  in.    Bound 
in   cloth.     Published  by  the  author.     Price,  40  cents. 
This  is  the  second  edition  of  this  book  published  by  the  author,  and 
contains    detailed    instructions    regarding    the    design,    construction    and 
the  operation  of  small  transformers.     With  these  instructions  a  trans- 
former for  110  or  220  volt  line  circuits  with  a  frequency  of  60  cycles 
can  be  stepped  down  to  a  minimum  of  eight  volts.     The  author  goes 
very    thoroughly    into   the    matter    of    construction,    and    shows    it    may 
be  built  'without  the  use  of  expensive  tools  or  machinery.    Transform- 
ers made  according  to  these  instructions  have  given  an  output  of   100 
watts   with   an  efficiency  of   over  90  per   cent. 

Price  Postpaid  in  Cloth,  40  Cents 

Remit  amount  with  order  to 

PROF.  F.  E.  AUSTIN,  Box  441,  Hanover,  New  Hampshire 


Directions  for  Designing,  Making  and 
Operating 

High  Pressure  Transformers 


Review  from  "Electrical  Engineering",  July,  1915. 

A  new  book  entitled  "DIRECTIONS  FOR  DESIGNING, 
MAKING  AND  OPERATING  HIGH  PRESSURE  TRANS- 
FORMERS," written  for  those  experimenters  who  desire  to  con- 
struct their  own  apparatus,  is  also  published  by  Prof.  F.  E.  Austin. 
This  book  is  a  companion  volume  of  "How  to  Make  a  Transformer 
for  Low  Pressures,"  but  containing  more  working  directions  and  use- 
ful talks  such  as  loss  due  to  Hysteresis,  per  cubic  inch  of  iron  core  for 
various  flux  densities  and  frequencies;  and  data  applying  to  copper 
magnet  wire.  The  book  is  well  illustrated  with  half-tone  and  line 
cuts  showing  special  methods  of  procedure,  fundamental  theories,  and 
finished  apparatus.  It  is  written  in  simple  English,  is  full  of  technical 
information  and  new  ideas  relating  to  methods  of  design  and  con- 
struction, and  will  prove  of  great  assistance  to  those  who  are  pursuing 
correspondence  courses  or  regular  college  courses.  The  price  of  the 
book  is  65  cents. 


K'eview    from   "Machinery",    May,   1915. 

Directions  for  Designing,  Making  and  Operating  High-Pressure 
Transformers.  By  F.  E.  Austin,  46  pages,  4^4  by  7l/2  inches,  21 
illustrations.  Published  by  Prof.  F.  E.  Austin,  Hanover,  N.  H. 

Price   65    cents. 

This  book  is  a.  companion  to  the  author's  work  on  making  a 
transformer  for  low  pressures.  It  describes  the  making  of  a  step-up 
transformer,  giving  20,000  volts,  for  wireless  telegraphs,  telephones, 
for  operating  tube  lamps  and  X-ray  tubes.  The  mathematical  matter 
is  treated  in'  a»  simple  way  that  is  well  within  the  comprehension  of 
the  amateur  who  would  be  interested  in  building  a  high-pressure  trans- 
former for  experimental  purposes.  All  materials  are  specified  and  all 
calculations  are  worked  out  for  the  model  described.  Probably  no 
exercise  would  give  the  average  student  a  firmer  grasp  of  electrical 
principles  than  the  building  of  a  piece  of  apparatus  like  this  trans- 
former. 

From  "Telephony",  Chicago,  Sept.  4,  1915: 

Directions  for  Designing,  Making  and  Operating  High-Pressure 
Transformers,  by  Prof.  F.  E.  Austin,  Hanover,  N.  H.  46  pages, 
4]/2  ins.  by  7^  ins.  with  illustrations.  Price,  cloth  binding,  65  cents. 

In  this  booklet,  points  relating  to  the  design  of  a  transformer  are 
first  taken  up,  after  which  the  practical  calculations  involved  are  con- 
sidered. Details  of  the  construction  of  a  three-kilowatt,  20,000-volt 
transformer  are  then  presented,  sketches  being  used  to  make  clear  the 
text.  Estimates  of  the  costs  of  materials  entering  into  the  construction 
of  transformers  according  to  the  design  presented  are  given. 

PROF.   F.   E.   AUSTIN, 

HANOVER,   N.   H., 
DEAR   PROF.   AUSTIN  : 

Your  two  little  books  on  transformers  received.  They  are  ex- 
ceptionally well  gotten  up.  I  was  pleased  to  get  them. 

Enclosed  you  will  find  check  paying  for  books  and  return  postage 
on  biii. 

1  trust  I  may  have  an  opportunity  of  using  more  of  your  books 
in  the  near  future. 

Yours  very  truly, 

ERNEST  C.  CHESWELL, 

Orono,  Maine 
(Instructor  in    Elec.    Eng.,   University  of   Maine) 

Nov.  5,  1915 

Price  bound  in  cloth,  post-paid  in  United  States,  65  cents.  Remit 
amount  with  order  to 

PROF.  F.  E.  AUSTIN,  Box  441,  Hanover,  N.  H. 


Your  Attention  is  Called  to  a 

NEW    DEPARTURE 

in  the   Book  Production,   entitled 

Examples  in  Alternating  -Currents 

By  PROF.  F.  E.  AUSTIN,  E.  E. 

A  valuable  book  for  students,  teachers  and  engineers. 

The  popularity  of  the  book  is  evident  from  the  fact  the  first 
edition  was  largely  subscribed  for  before  publication. 

FOR  STUDENTS:  The  application  of  fundamental  principles 
to  practice  is  aptly  illustrated  by  completely  worked  out  problems  ; 
the  process  of  solution  being  clearly  outlined  step  by  step.  Class 
room  problems  and  engineering  problems  are  fully  discussed. 

The    collection    of    useful    trigonometrical    formulae,    type    integral 

forms    and    tabulated    values    of     2  Tt'f,     ^         >  (2^/)2  and  To 


frequencies  from  1  to  150  cycles  is  alone  worth  many  times  the  price 
of  the  book. 

FOR  TEACHERS:  One  important  feature  of  the  book  affect- 
ing those  who  teach  the  important  theories  of  alternating-currents  to 
beginners,  is  that  of  so  clearly  and  definitely  fixing  important  mathe- 
matical processes  and  knowledge  of  physical  phenomena  in  the  stu- 
dent's mind,  that  instruction  may  resolve  itself  at  the  very  start  into 
emphasizing  engineering  application.  The  arrangement  of  the  prob- 
lems following  each  example,  some  with  and  some  without  answers, 
finds  favor  with  those  who  prefer  answers  to  problems,  as  well  as 
with  those  who  desire  problems  without  answers. 

FOR  ELECTRICAL  ENGINEERS:  Perhaps  the  chief  value 
of  the  book  to  electrical  engineers  lies  in  the  carefully  tabulated  ar- 
rangement of  mathematical  and  electrical  data;  useful  in  many  funda- 
mental considerations. 

FOR  NON-ELECTRICAL  ENGINEERS:  There  is  a  very 
large  class  of  engineers  not  directly  engaged  in  electrical  work,  but 
to  whom  a  practical  working  knowledge  of  alternating-currents  is  an 
essential  element  making  for  success.  Such  will  find  that  "Examples 
in  Alternating-Currents"  imparts  the  desired  information  in  a  mini- 
mum of  time. 

AS  A  REFERENCE  BOOK:  The  value  of  the  book  as  a  ref- 
erence book  for  all  classes  desiring  concise  and  exact  information  on 
electrical  matters  involving  the  principles  of  alternating-currents,  is 
greatly  enhanced  because  of  an  extensive  index,  referring  directly  to 
pages. 

PERMANENT  FEATURE:  The  discussions  throughout  the 
text,  dealing  as  they  do  with  fundamental  principles,  renders  the  in- 
formation of  permanent  value.  The  book  will  be  as  useful  twenty- 
five  years  hence,  as  it  is  today. 

ILLUSTRATIONS:  The  _  book  contains  carefully  arranged 
diagrams  of  electrical  circuits  with  corresponding  vector  diagrams  of 
pressure  and  current  components.  Many  diagrams  are  inserted  show- 
ing the  combination  of  sine-curve  alternating-quantities,  simple  appli- 
cations of  Calculus.,  and  the  derivation  of  fundamental  equations. 

Price  in  Flexible  Leather,  Pocket  Size,  $2.40 
Remit  amount  with  order  to  PROF.  F.  E.  AUSTIN,  Box  441,  Hanover,  N.  H. 


YOU   MAY   BE  INTERESTED 

in  the  following  "reviews"  of  "Examples  in  Alternating  Currents" 

Review  in  "Bulletin  of  the  Society  for  the  Promotion  of  Engi- 
neering Education",  October,  1915: 

Examples  in  Alternating  Currents.  Vol.  I.  By  F.  E.  Austin.  Pub- 
lished by  the  author  at  Hanover,  N.  H.  Price,  flexible  leather, 
$2.40. 

While  the  title  of  this  book  indicates  the  purpose,  it  by  no  means 
indicates  the  scope.  It  is  almost  a  text-book  in  its  treatment  of  alter- 
nating currents  and  alternating  current  circuits.  The  author  very 
evidently  had  in  mind  the  teacher,  the  student,  and  .the  practicing 
engineer  while  preparing  the  book. 

For  the  teacher  it  contains  a  well  ordered  list  of  problems  classi- 
fied under  the  proper  subheads ;  for  the  student  it  contains  in  addition 
to  explanatory  matter  covering  each  type  of  problem,  an  example 
completely  solved,  and  a  review  of  the  mathematics  involved ;  and  for 
the  practicing  engineer  it  furnishes  a  logically  planned  review  of  the 
whole  subject  of  alternating  quantities  and  the  solution  of  alternating 
current  circuits.  Some  unusual  tables  are  included.  The  calculus  is 
freely  used  and  the  fundamentals  of  calculus  and  trigonometry  are 
reviewed  as  they  become  necessary  to  the  solution  of  problems. 

L.   H.  H. 

Review  in  "Electrical  World"  of  October  23,  1915: 

Examples  in  Alternating   Currents.     Vol.    I.     By   Prof.   F.    E.   Austin. 

Published  by  the  author  at  Hanover,   N.   H.     224  pages,  69  illus. 

Price,  $2.40. 

The  author  of  this  work  has  made  a  very  successful  attempt  to 
help  the  student  and  practical  engineer  to  analyze  the  theory  underly- 
ing practical  problems  and  work  out  for  himself  certain  mathematical 
solutions.  The  problems  taken  up  deal  with  fundamental  principles 
of  alternating  currents  and  in  most  cases  are  worked  out  step  by  step. 
The  book  should  be  very  useful  to  teachers  as  a  class-room  text  for 
electrical  courses  and  to  engineers  as  a  reference  text,  since  it  con- 
tains numerous  formulas  and  several  useful  tables  designed  to  save, 
time  in  computations. 

"Telephony",   October   16,   1915: 

Examples  in  Alternating  Currents,  Vol.  I,  by  F.  E.  Austin,  Hanover, 
N.  H.;  223  pages  4^  ins.  by  7y2  ins.  with  70  illustrations  and  ta- 
bles. Price  $2.40. 

This  is  the  first  of  two  volumes  which  take  up  problems  'relating 
to  alternating  currents  such  as  are  encountered  in  engineering  prac- 
tice. In  this  volume  trigonometric  functions,  typical  expressions  en- 
countered in  integral  calculus,  and  their  application  in  the  study  of 
alternating  quantities  are  given. 

Practical  examples  are  worked  out  and  are  immediately  followed 
by  a  problem  which  may  be  solved  by  the  application  of  the  same 
methods.  The  first  thirty  examples  and  problems  relate  to  sine  and 
non-sine  curves  and  pressures,  after  which  inductance  is  taken  up. 


About  twenty  examples  and  problems  relating  to  inductance  are  pre- 
sented and  tbese  are  followed  by  a  discussion  of  resonance. 

A  feature  of  the  book'  is  the  inclusion  of  tables  containing  values 
of  variable  quantities  met  with  in  engineering  work,  arranged  to  ren- 
der evaluation  convenient  and  rapid.  One  of  the  tables  contains  values 
of  2irf  for  frequencies  from  1  to  151  cycles  and  other  corresponding 
values. 

While  the  book  is  intended  tc5  assist  the  college  student,  those  fol- 
lowing correspondence  courses  will  find  it  of  aid  to  them.  It  should 
also  be  of  value  to  the  practicing  engineer,  as  he  will  be  able  to  use 
the  results  of  the  solutions  of  the  problems  to  considerable  advantage. 


Some  idea  of  the  wide  field  covered  by  the  subject  matter  of  this 
book  may  be  obtained  from  the  following  letters: 

F.    JOS.     LAMB    CO. 

MANUFACTURERS    OF 

ELECTRIC  STARTERS 


DETROIT,  MICH.,  September  6,  1915 
PROF.  F.  E.  AUSTIN, 
Hanover,  N.  H., 

MY  DEAR  SIR  : — 

Your  letter  of  the  4th  instant  to  hand,  also  a  copy  of  your  new 
book  "Examples  in  Alternating  Currents".  I  wish  to  say  this  is  the 
best  book  on  the  subject  that  I  ever  saw,  and  I  believe  my  library  con- 
tains about  all  the  leading  books.  You  have  matter  in  this  book  which 
I  doubt  a  busy  man  like  myself  could  ever  "dig  out"  of  my  entire  list. 

I  attach  hereto  my  check  to  cover  its  cost,  also  for  another  copy 
I  want  you  to  send  to  a  friend  of  mine,  Mr  -  — ,  S.  C. 

Yours  very  sincerely, 

F.  Jos.  LAMB 


ADELPHI  COLLEGE 

BROOKLYN,  NEW  YORK 

September   25,    1915 
PROF.  F.  E.  AUSTIN, 
Hanover,  N.  H. 
DEAR  SIR:— 

I  would  acknowledge  with  thanks  your  Vol.  I,  Examples  in  Alter- 
nating Currents,  which  came  today.  I  have  already  read  enough  to 
see  its  value,  and  I  hope  your  return  from  it  will  be  satisfactory. 
There  is  need  of  a  book  on  this  subject.  Most  of  the  texts  are  quite 
meager. 

Very  sincerely  yours, 

(Signed)  W.   C.   PECKHAM 


,    October   22,    1915 
PROF.  F.  E.  AUSTIN, 
Hanover,  N.  H. 
DEAR  SIR: — 

I  have  reviewed  your  book,  and  found  it  well  worth  study. 
The  tables  in  the  back  of  the  book  are  well  worth  the  price  of  the 
volume,  and  the  problems  you  give  are  all  interesting  and  should  leave 
a  student  well  drilled  in  the  mathematics  of  the  subject. 

But   you    excel    everything   in    the    clearness    and    logical    order    of 
your   explanatory   sections. 

Very  truly  yours, 

CLINTON   C.   BARNES, 

Center    Rutland,   Vt., 
Electrical   Inspector  for  the  Vermont   Marble   Co, 


From  a  former  teacher  at  University  of  Pennsylvania: 

The  little  volume  is  a  beauty  from  every  point  of  view.  It  is 
without  doubt,  the  most  useful  and  helpful  book  for  use  in  the  study 
of  A.  C.  that  I  have  come  across.  It  is  in  a  class  by  itself,  without 
any  question. 

The  explanation  of  fundamental  theories,  the  mathematical  con- 
ception of  these  theories,  the  useful  data,  tabulated  formulae,  etc., 
and  the  extremely  clear  cuts^,  all  form  a  very  "complete  whole,"  which 
bespeaks  the  writer's  familiarity  with  the  subject,  and  the  students' 
view-point. 

Very   sincerely, 

WM.  F.  JOHNSON 


ELECTRICAL  ENGINEERING  DEPARTMENT 

IOWA  STATE  COLLEGE 

AMES,  IOWA 

FRED   A.    FISH.    PROFESSOR 

H.    C.    BARTHOLOMEW.    ASSOCIATE    PROFESSOR 

F.    A.     ROBBINS.    ASSISTANT    PROFESSOR 

Sept.   16,  1915 
PROF.  F.  E.  AUSTIN, 

HANOVER,  N.  H.,  • 
DEAR  SIR:— 

I   enclose   check   in   payment    for    "Examples    in  Alternating    Cur- 
rents."    I  am  very  much  pleased  with  it.     I   should  be  glad  to  have 

you  send  me  a  copy  of  Volume  II  as  soon  as  it  is  ready. 

Very  truly  yours, 

F.  A.  FISH 


YOU  CANNOT  AFFORD  TO  BE  WITHOUT  THIS  BOOK! 


I'kOl 

OKA  i 

and 

stink 


E) 


;T  ARTILLERY   SCHOOL, 

I-'MRT  JMm^QE,    VA. 

nv.      JO. 


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THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  5O  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


Currents" 

kind   of   a 

on  of  every 


=    SW     7    1932 


1934 


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Prof.  J 


SEF  S019J8 


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MAYS  11953  I 

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perfectly 
interesting 
nagnetism. 

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examples. 

:ematieally 

s   and   ap- 


.    $1.10 


5ox  441 


TJ)  21-20wi.fi '32 


316195 


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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


